We suggest an equilibrium concept for a strategic model with a large number of players in which each player observes the actions of only a small number of the other players. The concept fits well situations in which each player treats his sample as a prediction of the distribution of actions in the entire population, and responds optimally to this prediction. We apply the concept to a strategic voting model and investigate the conditions under which a centrist (...) candidate can win the popular vote although his strength in the population is smaller than the strengths of the right and left candidates.  2003 Elsevier Inc. All rights reserved. (shrink)

The theory of competition has held a central place in economic analysis since Adam Smith. This book, written by one of the most distinguished of contemporary economic theorists, reports on a major research program to provide strategic foundations for the theory of perfect competition. Beginning with a concise survey of how the theory of competition has evolved, Gale makes extensive and rigorous use of dynamic matching and bargaining models to provide a more complete description of how a competitive equlibrium (...) is achieved. Whereas economists have made use of a macroscopic description of markets in which certain behavioral characteristics, such as price-taking behavior, are taken for granted, Gale uses game theory to re-evaluate this assumption, beginning with individual agents and modelling their strategic interaction. A strategic foundation for competitive equilibrium shows how such interaction leads to competitive, price-taking behavior. Essential reading for graduate courses in game theory and general equilibrium. (shrink)

Over the past decade, the ideal model of shared decision-making has been increasingly promoted as the preferred standard of doctor-patient communication in medical consultation. The model advocates a treatment decision-making process in which the doctor and his patient are considered coequal partners that carefully negotiate the treatment options available in order to ultimately reach a treatment decision that is mutually shared. Thereby, the model notably leaves room for—and stimulates—argumentative discussions to arise in the context of medical consultation. A paradigm example (...) of a discussion that often emerges between doctors and their patients concerns antibiotics as a method of treatment for what is presumed to be a viral infection. Whereas the doctor will generally not encourage treatment with antibiotics, patients oftentimes prefer the medicine to other methods of treatment. In this paper, two cases of such antibiotic-related discussions in consultation are studied using insights gained in the extended pragma-dialectical theory to argumentation. It is examined how patient and physician maneuver strategically in order to maintain a balance between dialectical reasonableness and rhetorical effectiveness, as well as an equilibrium between patient participation and evidence-based medication, while arguing a case for and against antibiotics respectively. (shrink)

We propose a new game to strategically justify the constrained equal awards rule in claims problems. Our game is “procedurally fair” and “multilateral”. In addition, even if claimants cannot reach an agreement in any period, they can renegotiate in the next period. We show that, for each claims problem, the awards vector chosen by the constrained equal awards rule achieved at period 1 is the unique subgame perfect equilibrium outcome of the game.

In this concise book based on his Arne Ryde Lectures in 2002, Young suggests a conceptual framework for studying strategic learning and highlights theoretical developments in the area. He discusses the interactive learning problem; reinforcement and regret; equilibrium; conditional no-regret learning; prediction, postdiction, and calibration; fictitious play and its variants; Bayesian learning; and hypothesis testing. Young's framework emphasizes the amount of information required to implement different types of learning rules, criteria for evaluating their performance, and alternative notions of (...) equilibrium to which they converge. He also stresses the limits of what can be achieved: for a given type of game and a given amount of information, there may exist no learning procedure that satisfies certain reasonable criteria of performance and convergence. In short, Young has provided a valuable primer that delineates what we know, what we would like to know, and the limits of what we can know, when we try to learn about a system that is composed of other learners. (shrink)

Using a two-player Tullock-type contest, we show that intuitively and structurally different contests can be strategically equivalent. Strategically equivalent contests generate the same best response functions and, as a result, the same equilibrium efforts. However, strategically equivalent contests may yield different equilibrium payoffs. We propose a simple two-step procedure to identify strategically equivalent contests. Using this procedure, we identify contests that are strategically equivalent to the original Tullock contest, and provide new examples of strategically equivalent contests. Finally, we (...) discuss possible contest design applications and avenues for future theoretical and empirical research. (shrink)

We investigate how a group of players might cooperate with each other within the setting of a non-cooperative game. We pursue two notions of partial cooperative equilibria that follow a modification of Nash’s best response rationality rather than a core-like approach. Partial cooperative Nash equilibrium treats non-cooperative players and the coalition of cooperators symmetrically, while the notion of partial cooperative leadership equilibrium assumes that the group of cooperators has a first-mover advantage. We prove existence theorems for both types (...) of equilibria. We look at three well-known applications under partial cooperation. In a game of voluntary provision of a public good we show that our two new equilibrium notions of partial cooperation coincide. In a modified Cournot oligopoly, we identify multiple equilibria of each type and show that a non-cooperator may have a higher payoff than a cooperator. In contrast, under partial cooperation in a symmetric Salop City game, a cooperator enjoys a higher return. (shrink)

We study a first-price auction preceded by a negotiation stage with complete information, during which bidders may form a bidding ring. We prove that in the absence of externalities, the grand cartel forms in equilibrium, allowing ring members to gain the auctioned object for a minimal price. However, identity-dependent externalities may lead to the formation of small rings, as often observed in practice. Potential ring members may condition their participation on high transfer payments as a compensation for their expected (...) externalities if the ring forms. The cartel may therefore profitably exclude these bidders, although risking tougher competition in the auction. We also analyze ring efficiency in the presence of externalities, showing that a ring may prefer sending an inefficient member to the auction, if the efficient member exerts threatening externalities on bidders outside the ring, which in turn leads to a higher winning price. (shrink)

This paper examines the existence of strategic solutions to finite normal form games under the assumption that strategy choices can be described as choices among lotteries where players have security- and potential level preferences over lotteries (e.g., Cohen, Theory and Decision, 33, 101–104, 1992, Gilboa, Journal of Mathematical Psychology, 32, 405–420, 1988, Jaffray, Theory and Decision, 24, 169–200, 1988). Since security- and potential level preferences require discontinuous utility representations, standard existence results for Nash equilibria in mixed strategies (Nash, Proceedings (...) of the National Academy of Sciences, 36, 48–49, 1950a, Non-Cooperative Games, Ph.D. Dissertation, Princeton University Press, 1950b) or for equilibria in beliefs (Crawford, Journal of Economic Theory, 50, 127–154, 1990) do not apply. As a key insight this paper proves that non-existence of equilibria in beliefs, and therefore non-existence of Nash equilibria in mixed strategies, is possible in finite games with security- and potential level players. But, as this paper also shows, rationalizable strategies (Bernheim, Econometrica, 52, 1007–1028, 1984, Moulin, Mathematical Social Sciences, 7, 83–102, 1984, Pearce, Econometrica, 52, 1029–1050, 1984) exist for such games. Rationalizability rather than equilibrium in beliefs therefore appears to be a more favorable solution concept for games with security- and potential level players. (shrink)

We re-examine the relationship between coordination, legal sanctions, and free-riding in light of the recent controversy regarding the applicability of the coordination problem paradigm of law-making. We argue that legal sanctions can help solve coordination problems by eliminating socially suboptimal equilibrium outcomes. Once coordination has taken place, however, free-riding can not lead to the breakdown of coordination outcomes, even if sanctions may still be effective at increasing the equity of such outcomes. Finally, we argue that it is the choice (...) of a legal or constitutional system rather than the choice of law that is paradigmatic of the coordination problem. This view requires a re-assessment of the normative status of sanctions attached to individual laws. (shrink)

The difficulty of defining rational behavior in game situations is that the players'' strategies will depend on their expectations about other players'' strategies. These expectations are beliefs the players come to the game with. Game theorists assume these beliefs to be rational in the very special sense of beingobjectively correct but no explanation is offered of the mechanism generating this property of the belief system. In many interesting cases, however, such a rationality requirement is not enough to guarantee that an (...) equilibrium will be attained. In particular, I analyze the case of multiple equilibria, since in this case there exists a whole set of rational beliefs, so that no player can ever be certain that the others believe he has certain beliefs. In this case it becomes necessary to explicitly model the process of belief formation. This model attributes to the players a theory of counterfactuals which they use in restricting the set of possible equilibria. If it were possible to attribute to the players the same theory of counterfactuals, then the players'' beliefs would eventually converge. (shrink)

This book represents a major contribution to game theory. It offers this conception of equilibrium in games: strategic equilibrium. This conception arises from a study of expected utility decision principles, which must be revised to take account of the evidence a choice provides concerning its outcome. The argument for these principles distinguishes reasons for action from incentives, and draws on contemporary analyses of counterfactual conditionals. The book also includes a procedure for identifying strategic equilibria in ideal (...) normal-form games. In synthesizing decision theory and game theory in a powerful way this book will be of particular interest to all philosophers concerned with decision theory and game theory as well as economists and other social scientists. (shrink)

A strategic equilibrium is a profile of strategies that are each self-supporting given the profile. Strategic equilibria exist in games without Nash equilibria.

We develop a multi-agent deontic action logic to study the logical behaviour of two types of deontic conditionals: (1) conditional obligations, having the form "If group H were to perform action aH, then, in group F's interest, group G ought to perform action aG" and (2) conditional permissions, having the form "If group H were to perform action aH, then, in group F's interest, group G may perform action aG". First, we define a formal language for multi-agent deontic action logic (...) and a class of consequentialist models to interpret the formulas of the language. Second, we define a transformation that converts any strategic game into a consequentialist model. Third, we show that an outcome a* is a Nash equilibrium of a strategic game if and only if a conjunction of certain conditional permissions is true in the consequentialist model that results from the transformation of that strategic game. (shrink)

We develop a theory of joint intention in contexts in which participants have mixed motives that can manifest in all-things-considered reasons to deviate from contributing to the desired project, e.g., contexts with collective action problems. Our theory is based on strategic equilibrium-based reasoning, which links the characterization of joint intention in terms of individual intentions with conditions on strategy profiles of the underlying strategic games. We use elements of equilibrium reasoning to construct a counterfactual account of (...) joint intention in the mixed-motive contexts, which extends the reach of the notion of joint intention considerably beyond that of previous formulations. (shrink)

For strategic communication games à la Crawford and Sobel the paper shows that under some prior beliefs different equilibrium partitions of the state space can have equal cardinality. Hence, there can be different equilibrium action profiles with the same size.

Lying for a strategic advantage is to be expected in commercial interactions. But would this be more or less obvious when lying could come from either party and question mutually profitable exchange? To explore this, we modify the acquiring-a-company game by letting both, buyer and seller, be privately informed. Specifically, the value of the company for the buyer is known only by the seller; whereas, only the buyer is aware by which proportion the sellers evaluation is lower than that (...) of the buyer. Before bargaining, both parties can reveal what they know via cheap-talk numerical messages. Game theoretically, the pooling equilibrium may or may not allow for trade depending on the commonly known expected evaluation discrepancy. By mutually revealing what one knows, one could boost trade and efficiency. Although strategic misreporting prevails quite generally, it is higher for sellers throughout the experiment. Regarding gender, women misreport less, especially as sellers, and offer higher prices. (shrink)

The extent to which trust prevails can be measured by the subjective probability with which an agent expects another one to act in desired ways. An agent´s trust in other agents forms in repeated social interactions which typically have the structure of an elementary game of trust. The process of trust formation in such interactions may be described by a reputation function. It is argued that in view of real world processes of trust formation any adequate reputation function must satisfy (...) certain conditions. A simple model conforming to these conditions is presented. Analysing this example it is shown that there is a co-operative Nash equilibrium in a trust supergame which is in line with the basic conditions of trust formation. However, it is also proved that no process of trust formation can be reasonably similar to real world mechanisms and at the same time lead to subgame perfect equilibria in a trust supergame. (shrink)

This paper considers a one-stage Cournot duopoly of R&D. We characterize the Nash equilibrium of the one-stage game and provide a comparison with the two-stage version of the same Cournot model of R&D/product market competition. We look at R&D expenditures, profits, output and welfare. Under perfect symmetry, the one-stage model always leads to higher profits when the spillover parameter is not equal to 1/2. Moreover, the one-stage model implies more R&D expenditure and higher welfare if and only if the (...) spillover parameter is greater than 1/2. The insights are robust to an n -firm generalization, but the differences between the one-stage game and the two-stage game disappear as the market becomes perfectly competitive. (shrink)

We provide existence results in a game with local spillovers where the payoff function satisfies both convexity and the strategic substitutes property. We show that there always exists a stable pairwise network in this game, and provide a condition which ensures the existence of pairwise equilibrium networks.

The prelims comprise: Strategic Interaction Nash Equilibrium Normal‐form Refinements Games in Extensive Form Extensive‐form Refinements Selection by Evolution Notes.

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is (...) possible to explain cooperation in the one-shot Prisoner's Dilemma in a way that is in accordance with some recent experimental findings. (shrink)

Aiming at the two-echelon newsvendor problem in which the market demand of commodities is random both in normal sales period and in liquidation period, this paper studies the pricing and ordering decision of retailers by using rational expectation equilibrium under the condition of considering consumersʼ strategic behavior and rapid response mechanism. Then, the decision-making problem under retailersʼ initial order quantity commitment is discussed, as well as the effect of commitment mechanism on supply chain performance. On this basis, both (...) the two-part pricing contract and revenue-sharing contract are introduced to achieve supply chain coordination aiming at the profit maximization under the initial order quantity commitment mechanism. The results show that the rapid response mechanism can reduce the negative impact of consumers’ strategic behavior, and the initial order quantity commitment can further reduce the impact and improve the retailers’ profit. Both the two-part pricing contract and revenue-sharing contract can coordinate the whole supply chain in which the two-part pricing contract can distribute profit arbitrarily between manufacturers and retailers while the revenue-sharing contract can share risks among members of the supply chain. (shrink)

In this paper, we introduce a new approach to independent quantifiers, as originally introduced in Informational independence as a semantic phenomenon by Hintikka and Sandu [9] under the header of independence-friendly languages. Unlike other approaches, which rely heavily on compositional methods, we shall analyze independent quantifiers via equilibriums in strategic games. In this approach, coined equilibrium semantics, the value of an IF sentence on a particular structure is determined by the expected utility of the existential player in any (...) of the game’s equilibriums. This approach was suggested in Henkin quantifiers and complete problems by Blass and Gurevich [2] but has not been taken up before. We prove that each rational number can be realized by an IF sentence. We also give a lower and upper bound on the expressive power of IF logic under equilibrium semantics. (shrink)

With increasing market competition and rapid development of service economy, more and more enterprises are shifting from providing products or services to providing product-service systems that integrate products and services, in order to improve competitiveness and profitability. Meanwhile, consumers have strategic delayed purchasing behavior when purchasing the PSS and high requirements for service quality. This paper investigates the two-period pricing and service quality decisions of product-service supply chain considering consumers’ strategic behavior under decentralized and centralized scenarios. The (...) class='Hi'>equilibrium results are compared in two scenarios. In order to eliminate performance loss under the decentralized scenario, we design two-period dynamic contracts to coordinate the PSSC. Furthermore, numerical simulation is provided to verify the feasibility of the contracts. The following conclusions can be drawn: the higher the service input-efficiency, the more beneficial for alleviating consumers’ strategic purchase behavior under two scenarios, but this mitigation effect is more obvious under the centralized scenario. Compared with the centralized scenario, the service quality is lower, the two-period PSS sales prices are higher, and the two-period profit is lower under the decentralized scenario. The proportion of service valuation will promote the widening of the service quality gap under two scenarios, but in some cases, the service input-efficiency will weaken the promotion effect of the proportion of service valuation. The design of the two-period combined contracts depends on the proportion of service valuation. When the proportion of service valuation is high, the “two-period revenue sharing + service-cost sharing” combined dynamic contract can achieve PSSC perfect coordination. However, when the proportion of service valuation is low, it is necessary to design complexity combined dynamic contract which can achieve PSSC perfect coordination. (shrink)

Gupta has proposed a definition of strategic rationality cast in the framework of his revision theory of truth. His analysis, relative to a class of normal form games in which all players have a strict best reply to all other players’ strategy profiles, shows that game-theoretic concepts have revision-theoretic counterparts. We extend Gupta’s approach to deal with normal form games in which players’ may have weak best replies. We do so by adapting intuitions relative to Nash equilibrium refinements (...) to the revision-theoretic framework. We prove that there is a precise equivalence between trembling-hand perfect equilibria in two-player normal games and a revision-theoretic property. We then introduce lexicographic choice of action as a way to represent players’ expectations, which allows our analysis to reach full generality. Finally, we provide an example of the versatility of revision theory as applied to strategic interaction by formalizing a risk-and-compensation procedure of strategic choice in the revision-theoretic framework. (shrink)

In recent work, semantic games of independence-friendly logic were studied in strategic form in terms of Nash equilibria. The class of strategic games of independence-friendly logic is contained in the class of win-loss, zero-sum two-player games. In this note we draw on the theory of linear programming to develop tools to analyze the value of such games. We give two applications of these tools to independence-friendly logic under the so-called equilibrium semantics.

We consider a normal-form game in which there is a single exogenously given coalition of cooperating players that can write a binding agreement on pre-selected actions. The actions representing other dimensions of the strategy space remain under the sovereign, individual control of the players. We consider a standard extension of the Nash equilibrium concept denoted as a partial cooperative equilibrium as well as an equilibrium concept in which the coalition of cooperators has a leadership position. Existence results (...) are stated and we identify conditions under which the various equilibrium concepts are equivalent. We apply this framework to existing models of multi-market oligopolies and international pollution abatement. In a multi-market oligopoly, typically, a merger paradox emerges in the partial cooperative equilibrium. The paradox vanishes if the cartel attains a leadership position. For international pollution abatement treaties, cooperation by a sufficiently large group of countries results in a Pareto improvement over the standard tragedy of the commons outcome described by the Nash equilibrium. (shrink)

In this paper, I develop a syntactic framework for the analysis ofstrategic form games that is based on a straightforward combination ofstandard systems of doxastic, probabilistic and conditionalpropositional logic. In particular, for the probabilistic part I makeuse of the axiomatization provided in Fagin and Halpern (1994). The use ofconditionals allows to represent a strategic form game by a logicalformula in a very natural way. Also expected utility maximization can benaturally captured. I use this framework to prove a version of (...) a resulton Nash equilibrium conjectures first presented in Aumann and Brandenburger (1995). (shrink)

This paper uses a game-theoretic framework to formalize the Hayekian notion of equilibrium as the compatibility of plans. To do so, it imposes more structure on the conventional model of strategic games. For each player, it introduces goals, goal-oriented strategies, and the goals’ probabilities of success, from which players’ payoffs are derived. The differences between the compatibility of plans and Nash equilibrium are identified and discussed. Furthermore, it is shown that the notion of compatibility of plans, in (...) general, differs from the notion of Pareto efficiency. Since the compatibility of plans across all players can rarely be achieved in reality, a measurement is introduced to determine various degrees of plan compatibility. Several possible extensions and applications of the model are discussed. (shrink)

Axelord’s [(1970), Conflict of Interest, Markham Publishers, Chicago] index of conflict in 2 × 2 games with two pure strategy equilibria has the property that a reduction in the cost of holding out corresponds to an increase in conflict. This article takes the opposite view, arguing that if losing becomes less costly, a player is less likely to gamble to win, which means that conflict will be less frequent. This approach leads to a new power index and a new measure (...) of stubbornness, both anchored in strategic reasoning. The win probability defined as power constitutes an equilibrium refinement which differs from Harsanyi and Selten’s [(1988), A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge] refinement. In contrast, Axelrod’s approach focuses on preferences regarding divergences from imaginary outmost rewards that cannot be obtained jointly. The player who is less powerful in an asymmetric one-shot game becomes more powerful in the repeated game, provided he or she values the future sufficiently more than the opponent. This contrasts with the view that repetition induces cooperation, but conforms with the expectation that a more patient player receives a larger share of the pie. (shrink)

This book represents a major contribution to game theory. It offers this conception of equilibrium in games: strategic equilibrium. This conception arises from a study of expected utility decision principles, which must be revised to take account of the evidence a choice provides concerning its outcome. The argument for these principles distinguishes reasons for action from incentives, and draws on contemporary analyses of counterfactual conditionals. The book also includes a procedure for identifying strategic equilibria in ideal (...) normal-form games. In synthesizing decision theory and game theory in a powerful way this book will be of particular interest to all philosophers concerned with decision theory and game theory as well as economists and other social scientists. (shrink)

Strong Nash equilibrium and coalition-proof Nash equilibrium rely on the idea that players are allowed to form coalitions and make joint deviations. Both of these notions consider cases in which any coalition can be formed. Accordingly, there may arise “conflicts of interest” that prevent a player from choosing an action that simultaneously meets the requirements of two coalitions to which he or she belongs. Here, we address this observation by studying an organizational framework such that the coalitional structure (...) is motivated by real-life examples where players cannot form some coalitions and formulated in such a way that no conflicts of interest remain. We define an organization as an ordered collection of partitions of the player set such that any partition is coarser than the partitions that precede it. For any given organization, we introduce the notion of organizational Nash equilibrium. We analyze the existence of equilibrium in a subclass of games with strategic complementarities and illustrate how the proposed notion refines the set of Nash equilibria in some examples of normal form games. (shrink)

Since the seminal paper of Nash (Proc Natl Acad Sci USA 36:48–49, 1950) game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. In a recent paper of Pruzhansky (Int J Game Theory 40:351–365, 2011) it was shown that under fairy general conditions maximin strategies in completely mixed games can guarantee the same expected payoff as completely mixed Nash equilibrium strategies. Based on this finding, the current paper argues that maximin strategies have important properties. (...) For instance, maximin strategies may refine Nash equilibria in subjective mixed strategies. Further, Bayesian rationality of the players may favor maximin strategies more often than Nash equilibrium strategies. The paper concludes with several suggestions for further experimental research that may shed more light on whether maximin behavior can explain reality better than Nash equilibrium. (shrink)

In this paper we examine optimal bidding without the independence axiom in a unified framework which allows for a clear graphical representation. Thus, we can show very simply the independence axiom to be a necessary and sufficient condition on preferences for strategical equivalence of the two first-price and second-price auctions, respectively, and for the second-price sealed-bid auction to be demand revealing. The analysis reveals that the betweenness property is necessary and sufficient for the ascending-bid auction to be demand revealing while (...) optimal bids exceed (are less than) bidders' valuations, iff preferences are quasiconcave (quasiconvex). Furthermore, it can be shown that fanning out (fanning in) leads to a higher (lower) selling-price in open than in sealed-bid auctions. (shrink)

David Gauthier develops morality in the social contract tradition as an emergent property rationally necessitated by the presence of inefficiency. To demarcate situations in which morality arises from those in which it does not, two principles, Strategic Emergence and Market Emergence, are motivated and assumed by Gauthier to be equivalent. Following the work of Bob Bright, this paper formalizes and expands upon a demonstration of the inconsistency of the two principles. Eliminating each of the emergence conditions is considered to (...) resolve the inconsistency. Additionally, the Kantian equilibrium is examined in place of the Nash equilibrium; however, Gauthier’s approach resists such amendments. (shrink)

Morality is concerned with interaction among persons, and so with strategic choice, in which each adopts a strategy on the basis of what he expects others to do. We state three conditions of strategically rational choice, and show that on the maximizing conception of rationality they require the expected outcome of interaction to be in equilibrium, so that each person's choice is a maximizing response to the choices of the others. We mention Nash's proof that in any finite (...) situation, there is at least one set of equilibrium strategies, but we then introduce the well‐known result, exemplified by the Prisoner's Dilemma, that, in many situations, no set of equilibrium strategies achieves optimality. In such situations, everyone could benefit were they to interact, not on the basis of individual utility maximization, but on a basis that would yield an optimal outcome. (shrink)

It is usually assumed in game theory that agents who interact strategically with each other are rational, know the strategies open to other agents as well as their payoffs and, moreover, have common knowledge of all the above. In some games, that much information is sufficient for the players to identify a "solution" and play it. The most commonly adopted solution concept is that of Nash equilibrium. A Nash equilibrium is defined a combination of strategies, one for each (...) player, such that no player can profit from a deviation from his strategy if the opponents stick to their strategies. Nash equilibrium is taken to have predictive power, in the sense that in order to predict how rational agents will in fact behave, it is enough to identify the equilibrium patterns of actions. Barring the case in which players have dominant strategies, to play her part in a Nash equilibrium a player must believe that the other players play their part, too. But an intelligent player must immediately realize that she has no ground for this belief. Take the case of a one-shot, simultaneous game. Here all undominated strategies are possible choices, and the beliefs supporting them are possible beliefs, even if this game has a.. (shrink)

The paper argues that the Nash Equilibrium Refinement Programme was less successful than its competitor, the Epistemic Programme. The prime criterion of success is the extent to which the programmes were able to reach the key objective guiding non-cooperative game theory for much of the twentieth century, namely, to develop a complete characterisation of the strategic rationality of economic agents in the form of the ultimate solution concept for any normal form and extensive game. The paper explains this (...) in terms of unjustified degrees of mathematisation in Nash Equilibrium Refinement Programme. While this programme’s mathematical models were often inspired by purely mathematical concerns rather than the economic phenomena they were intended to model, the Epistemic Programme’s models were developed with a keen eye to the role beliefs and desires play in strategic interaction between rational economic agents playing games; that is, their interactive epistemology. The Epistemic Programme succeeded in developing mathematical models formalising aspects of strategic interaction that remained implicit in the Nash Equilibrium Refinement Programme owing to an unjustified degree of mathematisation. As a result, the Epistemic Programme is the more successful theory.Keywords: Epistemic Programme; Game theory; Interactive epistemology; Mathematisation; Nash equilibrium. (shrink)

The article studies properties of interchangeability of pure, mixed, strict, and strict mixed Nash equilibria. The main result is a sound and complete axiomatic system that describes properties of interchangeability in all four settings. It has been previously shown that the same axiomatic system also describes properties of independence in probability theory, nondeducibility in information flow, and non-interference in concurrency theory.

It is well known that Nash equilibria may not be Pareto-optimal; worse, a unique Nash equilibrium may be Pareto-dominated, as in Prisoners’ Dilemma. By contrast, we prove a previously conjectured result: every finite normal-form game of complete information and common knowledge has at least one Pareto-optimal nonmyopic equilibrium (NME) in pure strategies, which we define and illustrate. The outcome it gives, which depends on where play starts, may or may not coincide with that given by a Nash (...) class='Hi'>equilibrium. We use some simple examples to illustrate properties of NMEs—for instance, that NME outcomes are usually, though not always, maximin—and seem likely to foster cooperation in many games. Other approaches for analyzing farsighted strategic behavior in games are compared with the NME analysis. (shrink)

Game-theoretic solution concepts describe sets of strategy profiles that are optimal for all players in some plausible sense. Such sets are often found by recursive algorithms like iterated removal of strictly dominated strategies in strategic games, or backward induction in extensive games. Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. In this paper, we propose a different perspective, analyzing solution algorithms as processes of (...) learning which change game models. Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. This dynamic stance provides a new look at the current interface of games, logic, and computation. (shrink)

Kevin Sauvé has recently argued in this journal that David Gauthier's conception of ‘morals by agreement’ is inimical to the development of long-term productive investment and sustainable levels of resource exploitation. According to Sauvé, this is because society is confronted with an intergenerational interaction problem whose strategic equilibrium is suboptimal. However, unlike the ‘contemporaneous Prisoner's Dilemma’ that Gauthier analyzes, the intergenerational version cannot be solved by an appeal to constrained maximization. As a result, Sauvé claims, Gauthier cannot effectively (...) address the question of intergenerational justice.The portion of Sauvé's argument that concerns me is the following:Gauthier solves the contemporaneous Prisoner's Dilemma by ensuring that each person will cooperate only if all others cooperate, and indeed his conception of morality is aimed at ensuring that all individuals incur the costs as well as the benefits of social cooperation. But the contemporaneous solution cannot be applied to the Intergenerational Dilemma: if each generation will save for the next only if the previous generations have also saved, none will ever save. (shrink)

AI companies are racing to create artificial general intelligence, or “AGI.” If they succeed, the result will be human-level AI systems that can independently pursue high-level goals by formulating and executing long-term plans in the real world. Leading AI researchers agree that some of these systems will likely be “misaligned”–pursuing goals that humans do not desire. This goal mismatch will put misaligned AIs and humans into strategic competition with one another. As with present-day strategic competition between nations with (...) incompatible goals, the result could be violent and catastrophic conflict. Existing legal institutions are unprepared for the AGI world. New foundations for AGI governance are needed, and the time to begin laying them is now, before the critical moment arrives. -/- This Article begins to lay those new legal foundations. It is the first to think systematically about the dynamics of strategic competition between humans and misaligned AGI. The Article begins by showing, using formal game-theoretic models, that, by default, humans and AIs will be trapped in a prisoner’s dilemma. Both parties’ dominant strategy will be to permanently disempower or destroy the other, even though the costs of such conflict would be high. -/- The Article then argues that a surprising legal intervention could transform the game theoretic equilibrium and avoid conflict: AI rights. Not just any AI rights would promote human safety. Granting AIs the right not to be needlessly harmed–as humans have granted to certain non-human animals–would, for example, have little effect. Instead, to promote human safety, AIs should be given those basic private law rights–to make contracts, hold property, and bring tort claims–that law already extends to non-human corporations. Granting AIs these economic rights would enable long-run, small-scale, mutually-beneficial transactions between humans and AIs. This would, we show, facilitate a peaceful strategic equilibrium between humans and AIs for the same reasons economic interdependence tends to promote peace in international relations. Namely, the gains from trade far exceed those from war. Throughout, we argue that human safety, rather than AI welfare, provides the right framework for developing AI rights. This Article explores both the promise and the limits of AI rights as a legal tool for promoting human safety in an AGI world. (shrink)

We use game theory and Santa Fe Artificial Stock Market, an agent-based model of an evolving stock market, to study the optimal frequency for traders to revise their market forecasting rules. We discover two things: There is a unique strategic Nash equilibrium in the game of choosing forecast revision rates, and this equilibrium is sub-optimal in the sense that traders’ earnings are not maximized an the market is inefficient. This strategic equilibrium is due to an (...) analogue of the prisoner’s dilemma; the optimal global state is unstable because each trader has too much incentive to ‘defect’ and use forecasting rules that pull the market into thesub-optimal equilibrium. (shrink)

There seems to be a difference between drinking coffee alone at home and drinking coffee in a café. Yet, drinking coffee in a café is not a joint action. It is an individual action done in a social environment. The café, with each person minding their own business next to others, is what I call a gregarious state of affairs. Gregariousness refers to the warmth of the social world. It is the difference between studying alone at home and studying in (...) the library. This light form of sociality is precisely what we were deprived of during the coronavirus lockdowns. Gregariousness cannot be explained as interaction or coordination, and neither can it be grasped solely as a normative aspect of the environment. This is why gregariousness cannot be explained using the concepts of strategic equilibrium, shared planning agency, joint commitment, we-intention, or second-person standpoint. In this paper, I will also provide a prospective theory of gregariousness. The aim of this paper is not to provide a definitive theory of gregariousness, nor to demonstrate that other theories of joint action are incorrect, but rather to draw attention to this aspect of the social world that has been largely neglected. (shrink)

This paper studies the three kinds of conservativeness in a jury decision-making structure: the voting rule, the threshold of reasonable doubt, and the legal information system. In a model of simultaneous voting, Feddersen and Pesendorfer (The American Political Science Review, 92(1), 23-35, 1998) argue that the unanimity rule is the worst-performing voting rule because voters with strategic behaviour mitigate the bias brought about by the voting rule. If this bias can be offset by an opposing (less conservative) bias in (...) the legal information system, we would be able to restore the rationality of informative voting. The new informative equilibrium is strictly better than the original strategic equilibrium in terms of ex post error probability. When a strategic equilibrium survives, we can lower the probability of convicted defendant being innocent by making the information system more informative or by forming a jury with a higher (more conservative) threshold of reasonable doubt. (shrink)

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based voting”, (...) which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

Nash Equilibrium is a central concept ingame theory. It has been argued that playing NashEquilibrium strategies is rational advice for agentsinvolved in one-time strategic interactions capturedby non-cooperative game theory. This essaydiscusses arguments for that position: vonNeumann–Morgenstern's argument for their minimaxsolution, the argument from self-enforcingagreements, the argument from the absence ofprobabilities, the transparency-of-reasons argument,the argument from regret, and the argument fromcorrelated equilibrium. All of these argumentseither fail entirely or have a very limited scope.Whatever the use of Nash (...) class='Hi'>Equilibrium is, therefore,it is not useful as a rational recommendation inone-time strategic interactions. This is good newsfor Bayesians: although this discussion does notargue directly for the Bayesian idea of rationalityas expected utility maximization, it argues againsta position that has been regarded as a contender insituations of strategic interaction. (shrink)