Two examples demonstrate the possibility of extremely complicated non-convergent behavior in evolutionary game dynamics. For the Taylor-Jonker flow, the stable orbits for three strategies were investigated by Zeeman. Chaos does not occur with three strategies. This papers presents numerical evidence that chaotic dynamics on a strange attractor does occur with four strategies. Thus phenomenon is closely related to known examples of complicated behavior in Lotka-Volterra ecological models.

This paper discusses the explanatory significance of the equilibrium concept in the context of an example of extremely complicated dynamical behavior. In particular, numerical evidence is presented for the existence of chaotic dynamics on a "strange attractor" in the evolutionary game dynamics introduced by Taylor and Jonker [also known as the "replicator dynamics"]. This phenomenon is present already in four strategy evolutionary games where the dynamics takes place in a simplex in three dimensional space-the lowest (...) number of dimensions in which such a strange attractor is possible. From a dynamical point of view, it is the attractor-rather than the equilibrium-that is of prime interest. (shrink)

Dynamo: Diagrams for Evolutionary Game Dynamics is free, open-source software used to create phase diagrams and other images related to dynamical systems from evolutionary game theory. We describe how to use the software’s default settings to generate phase diagrams quickly and easily. We then explain how to take advantage of the software’s intermediate and advanced features to create diagrams that highlight the key properties of the dynamical system under study. Sample code and output are provided to help (...) demonstrate the software’s capabilities. (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)

We continue the work initiated in Herzig and Lorini (J Logic Lang Inform, in press) whose aim is to provide a minimalistic logical framework combining the expressiveness of dynamic logic in which actions are first-class citizens in the object language, with the expressiveness of logics of agency such as STIT and logics of group capabilities such as CL and ATL. We present a logic called ( Deterministic Dynamic logic of Agency ) which supports reasoning about actions and joint actions of (...) agents and coalitions, and agentive and coalitional capabilities. In it is supposed that, once all agents have selected a joint action, the effect of this joint action is deterministic. In order to assess we prove that it embeds Coalition Logic. We then extend with modal operators for agents’ preferences, and show that the resulting logic is sufficiently expressive to capture the game-theoretic concepts of best response and Nash equilibrium. (shrink)

We discuss games of both perfect and imperfect information at two levels of structural detail: players’ local actions, and their global powers for determining outcomes of the game. We propose matching logical languages for both. In particular, at the ‘action level’, imperfect information games naturally model a combined ‘dynamic-epistemic language’ – and we find correspondences between special axioms and particular modes of playing games with their information dynamics. At the ‘outcome level’, we present suitable notions of game (...) equivalence, plus some simple representation results. (shrink)

Internet services, such as review sites, FAQ sites, online auction sites, online flea markets, and social networking services, are essential to our daily lives. Each Internet service aims to promote information exchange among people who share common interests, activities, or goods. Internet service providers aim to have users of their services actively communicate through their services. Without active interaction, the service falls into disuse. In this study, we consider that an Internet service has a network externality as its main feature, (...) and we model user behavior in the Internet service with network externality as a dynamic game. In particular, we model the diffusion process of users of an ISNE as an infinite-horizon extensive-form game of complete information in which: each user can choose whether or not to use the ISNE in her/his turn and the network effect of the ISNE depends on the history of each player’s actions. We then apply Markov perfect equilibrium to analyze how to increase the number of active users. We derive the necessary and sufficient condition under which the state in which every player is an active user is the unique Markov perfect equilibrium outcome. Moreover, we propose an incentive mechanism that enables the number of active users to increase steadily. (shrink)

In this paper I present a dynamic-epistemic hybrid logic for reasoning about information and intention changes in situations of strategic interaction. I provide a complete axiomatization for this logic, and then use it to study intentions-based transformations of decision problems.

Transfer of information between senders and receivers, of one kind or another, is essential to all life. David Lewis introduced a game theoretic model of the simplest case, where one sender and one receiver have pure common interest. How hard or easy is it for evolution to achieve information transfer in Lewis signaling?. The answers involve surprising subtleties. We discuss some if these in terms of evolutionary dynamics in both finite and infinite populations, with and without mutation.

We study the handicap principle in terms of the Sir Philip Sidney game. The handicap principle asserts that cost is required to allow for honest signalling in the face of conflicts of interest. We show that the significance of the handicap principle can be challenged from two new directions. Firstly, both the costly signalling equilibrium and certain states of no communication are stable under the replicator dynamics ; however, the latter states are more likely in cases where honest (...) signalling should apply. Secondly, we prove the existence and stability of polymorphisms where players mix between being honest and being deceptive and where signalling costs can be very low. Neither the polymorphisms nor the states of no communication are evolutionarily stable, but they turn out to be more important for standard evolutionary dynamics than the costly signalling equilibrium. (shrink)

In this paper, we study the structural optimization of community governance in smart cities and optimize the structure based on the game analysis of dynamic planning evolution. Theoretically, the connotation and extension of the concept of “self-organization” are cleared, and the environment and conditions of community self-organization formation, the formation process of community self-organization, and the types of community self-organization are discussed. The so-called “self-organization” is a process of spontaneously moving from disorder to order, and the environment and conditions (...) of community self-organization are mainly the openness, nonequilibrium state, and nonlinearity of the system. The key parameters of the contract with the change of the values of each factor make up for the inability to collect data for the empirical study in this paper; then, it presents four linear stages along with the cause such as self-creation, self-expansion, self-maintenance, and self-degeneration, respectively. The types of community self-organization mainly include community self-organization with random aggregation, socialized community self-organization, and stable community self-organization with autonomy orientation. By systematically sorting out the relationship between community self-organization and government, while confirming the positive significance of community self-organization to community cultural governance, various complex conflicts and game relationships will deeply affect the actual effectiveness of cultural governance and provide useful knowledge reference for future community cultural governance. (shrink)

Passive Brain-Computer interfaces (pBCIs) are a human-computer communication tool where the computer can detect from neurophysiological signals the current mental or emotional state of the user. The system can then adjust itself to guide the user towards a desired state. One challenge facing developers of pBCIs is that the system's parameters are generally set at the onset of the interaction and remain stable throughout, not adapting to potential changes over time such as fatigue. The goal of this paper is to (...) investigate the improvement of pBCIs with settings adjusted according to the information provided by a second neurophysiological signal. With the use of a second signal, making the system a hybrid pBCI, those parameters can be continuously adjusted with dynamic thresholding to respond to variations such as fatigue or learning. In this experiment, we hypothesize that the adaptive system with dynamic thresholding will improve perceived game experience and objective game performance compared to two other conditions: an adaptive system with single primary signal biocybernetic loop and a control non-adaptive game. A within-subject experiment was conducted with 16 participants using three versions of the game Tetris. Each participant plays 15 minutes of Tetris under three experimental conditions. The control condition is the traditional game of Tetris with a progressive increase in speed. The second condition is a cognitive load only biocybernetic loop with the parameters presented in Ewing et al. (2016). The third condition is our proposed biocybernetic loop using dynamic threshold selection. Electroencephalography was used as the primary signal and automatic facial expression analysis as the secondary signal. Our results show that, contrary to our expectations, the adaptive systems did not improve the participants' experience as participants had more negative affect from the BCI conditions than in the control condition. We endeavored to develop a system that improved upon the authentic version of the Tetris game, however, our proposed adaptive system neither improved players’ perceived experience, nor their objective performance. Nevertheless, this experience can inform developers of hybrid passive BCIs on a novel way to employ various neurophysiological features simultaneously. (shrink)

A systematic, rigorous, comprehensive, and unified overview of evolutionary game theory.

We present a dynamic model of the evolution of communication in a Lewis signaling game while systematically varying the degree of common interest between sender and receiver. We show that the level of common interest between sender and receiver is strongly predictive of the amount of information transferred between them. We also discuss a set of rare but interesting cases in which common interest is almost entirely absent, yet substantial information transfer persists in a *cheap talk* regime, and offer (...) a diagnosis of how this may arise. -/- . (shrink)

This paper proposes a Cournot game organized by three competing firms adopting bounded rationality. According to the marginal profit in the past time step, each firm tries to update its production using local knowledge. In this game, a firm’s preference is represented by a utility function that is derived from a constant elasticity of substitution production function. The game is modeled by a 3-dimensional discrete dynamical system. The equilibria of the system are numerically studied to detect their (...) complex characteristics due to difficulty to get an explicit form for those equilibria. For the proposed utility function, some cases with different value parameters are considered. Numerical simulations are used to provide an experimental evidence for the complex behavior of the evolution of the system. The obtained results show that the system loses its stability due to different types of bifurcations. (shrink)

Despite the challenges associated with virtually mediated communication, remote collaboration is a defining characteristic of online multiplayer gaming communities. Inspired by the teamwork exhibited by players in first-person shooter games, this study investigated the verbal and behavioral coordination of four-player teams playing a cooperative online video game. The game, Desert Herding, involved teams consisting of three ground players and one drone operator tasked to locate, corral, and contain evasive robot agents scattered across a large desert environment. Ground players (...) could move throughout the environment, while the drone operator’s role was akin to that of a “spectator” with a bird’s-eye view, with access to veridical information of the locations of teammates and the to-be-corralled agents. Categorical recurrence quantification analysis was used to measure the communication dynamics of teams as they completed the task. Demands on coordination were manipulated by varying the ground players’ ability to observe the environment with the use of game “fog.” Results show that catRQA was sensitive to changes to task visibility, with reductions in task visibility reorganizing how participants conversed during the game to maintain team situation awareness. The results are discussed in the context of future work that can address how team coordination can be augmented with the inclusion of artificial agents, as synthetic teammates. (shrink)

Outcomes of interspecific competition, and especially the possibility of coexistence, have been extensively studied in theoretical ecology because of their implications in community assemblages. During the last decades, the influence of different time scales through the local/regional dynamics of animal communities has received an increasing attention. Nevertheless, different time scales involved in interspecific competition can result form other processes than spatial dynamics. Here, we envision and analyze a new theoretical framework that couples a game theory approach for (...) competition with a demographic model. We take advantage of these two time scales to derive a reduced model governing the total densities of the two populations and we study how these two time scales interfere and influence outcomes of species competition. We find that a competition process occurring on a faster time scale than demography yields a “priority effect” where the first species introduced outcompetes the other one. We then confirm previous findings stipulating that species coexistence is favored by large difference in time scales because the extinction/recolonization process. Our results then highlight that an integration of demographic and competition time scales at both local and regional levels is mandatory to explain communities assemblages and should become a research priority. (shrink)

We make a proposal for formalizing simultaneous games at the abstraction level of player’s powers, combining ideas from dynamic logic of sequential games and concurrent dynamic logic. We prove completeness for a new system of ‘concurrent game logic’ CDGL with respect to finite non-determined games. We also show how this system raises new mathematical issues, and throws light on branching quantifiers and independence-friendly evaluation games for first-order logic.

Skyrms' investigations of dynamic deliberation are traced through his book of 1990 and his subsequent investigation of dynamic deliberation based on inductive rules to his recent results about chaos generated by evolutionary game dynamics. It is argued that the dynamics studied in the book, and the inductive dynamics as well, need to be supplemented to yield the correct recommendation in an example game. Some features about information feedback are pointed out. Finally, it is suggested that (...) more work is needed to assess whether Skyrms' results about chaos have any interesting implications for plausible game theoretic representations of interactions among human agents. (shrink)

We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief (...) over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing probabilistic “action models” and proposing a notion of probabilistic update product, that comes together with appropriate reduction laws. (shrink)

Logic is breaking out of the confines of the single-agent static paradigm that has been implicit in all formal systems until recent times. We sketch some recent developments that take logic as an account of information-driven interaction. These two features, the dynamic and the social, throw fresh light on many issues within logic and its connections with other areas, such as epistemology and game theory.

The language we use over the course of conversation changes as we establish common ground and learn what our partner finds meaningful. Here we draw upon recent advances in natural language processing to provide a finer‐grained characterization of the dynamics of this learning process. We release an open corpus (>15,000 utterances) of extended dyadic interactions in a classic repeated reference game task where pairs of participants had to coordinate on how to refer to initially difficult‐to‐describe tangram stimuli. We (...) find that different pairs discover a wide variety of idiosyncratic but efficient and stable solutions to the problem of reference. Furthermore, these conventions are shaped by the communicative context: words that are more discriminative in the initial context (i.e., that are used for one target more than others) are more likely to persist through the final repetition. Finally, we find systematic structure in how a speaker's referring expressions become more efficient over time: Syntactic units drop out in clusters following positive feedback from the listener, eventually leaving short labels containing open‐class parts of speech. These findings provide a higher resolution look at the quantitative dynamics of ad hoc convention formation and support further development of computational models of learning in communication. (shrink)

This book develops a view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book (...) develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science. (shrink)

Accurately predicting other people's actions may involve two processes: internal real-time simulation (dynamic updating) and matching recently perceived action images (static matching). Using a priming of body parts, this study aimed to differentiate the two processes. Specifically, participants played a motion-controlled video game with either their arms or legs. They then observed arm movements of a point-light actor, which were briefly occluded from view, followed by a static test pose. Participants judged whether this test pose depicted a coherent continuation (...) of the previously seen action (i.e., “action prediction task”). Evidence of dynamic updating was obtained after compatible effector priming (i.e., arms), whereas incompatible effector priming (i.e., legs) indicated static matching. Together, the results support action prediction as engaging two distinct processes, dynamic simulation and static matching, and indicate that their relative contributions depend on contextual factors like compatibility of body parts involved in performed and observed action. (shrink)

Immersion in video games is a complex psychological process often defined as a unitary phenomenon, but it actually takes at least a dual form, as video games encompass both narratives and simulations. This study aimed to understand the relationship between sensory and mental immersive experiences in video game play. A mixed-methods, interview-based study was conducted with eight dedicated players. Phenomenological analysis revealed a dynamic relationship between sensory and mental immersion, with one type sometimes becoming dominant or both combining and (...) transitioning throughout gameplay. Recognizing and measuring these distinct experiences is crucial for advancing video game scholarship and understanding the effects of gameplay. (shrink)

We study the dynamics and stability of the economics of crime and punishment game from an evolutionary perspective. Specifically, we model the interaction between agents and controllers as an asymmetric game exploring the dynamics of the classic static model using a replicator dynamics equation, given exogenous levels of monitoring and criminal sanctions. The dynamics show five possible equilibria, from which three are stable. Our results show that a culture of honest agents is never stable; (...) however when the penalty is high enough, the system will neutrally tend to an equilibrium of honest agents and a monitoring firm. By contrast, when the probability of detecting wrongdoing is small, the system, in some cases, will remain in a transient state, in which it is impossible to predict the proportion of honest agents. (shrink)

Millions of scientific articles are published each year, making it difficult to stay abreast of advances within even the smallest subdisciplines. Traditional approaches to the study of science, such as the history and philosophy of science, involve closely reading a relatively small set of journal articles. And yet many questions benefit from casting a wider net: Is most scientific change gradual or revolutionary? What are the key sources of scientific novelty? Over the past several decades, a massive effort to digitize (...) the academic literature and equip computers with algorithms that can distantly read and analyze a digital database has taken us one step closer to answering these questions. The Dynamics of Science brings together a diverse array of contributors to examine the largely unexplored computational frontiers of history and philosophy of science. Together, they reveal how tools and data from automated textual analysis, or machine "reading," combined with methods and models from game theory and cultural evolutionary theory, can begin to answer fundamental questions about the nature and history of science. (shrink)

Many different approaches to describing the players’ knowledge and beliefs can be found in the literature on the epistemic foundations of game theory. We focus here on non-probabilistic approaches. The two most prominent are the so-called Kripkeor Aumann- structures and knowledge structures (non-probabilistic variants of Harsanyi type spaces). Much of the recent work on Kripke structures has focused on dynamic extensions and simple ways of incorporating these. We argue that many of these ideas can be applied to knowledge structures (...) as well. Our main result characterizes precisely when one type can be transformed into another type by a specific type of information update. Our work in this paper suggest that it would be interesting to pursue a theory of “information dynamics” for knowledge structures (and eventually Harsanyi type spaces). (shrink)

A quadratic utility function is introduced in this paper to study the dynamic characteristics of Cournot duopoly game. Based on the bounded rationality mechanism, a discrete dynamical map that describes the game’s dynamic is obtained. The map possesses only one equilibrium point which is Nash point. The stability conditions for this point are analyzed. These conditions show that the point becomes unstable due to two bifurcation types that are flip and Neimark–Sacker. The synchronization property for that map is (...) studied. Through local and global analysis, some dynamics of attracting sets are investigated. This analysis gives some insights on the basis of those sets and the shape of the critical curves. It also shows some lobes found in those attracting sets which are constructed due to the origin focal point. (shrink)

Within the context of extensive-form (or dynamic) games, we use choice frames to represent the initial beliefs of a player as well as her disposition to change those beliefs when she learns that an information set of hers has been reached. As shown in [5], in order for the revision operation to be consistent with the AGM postulates [1], the player’s choice frame must be rationalizable in terms of a total pre-order on the set of histories. We consider four properties (...) of choice frames and show that, together with the hypothesis of a common prior, are necessary and sufficient for the existence of a plausibility order that rationalizes the epistemic state (that is, initial beliefs and disposition to revise those beliefs) of all the players. The plausibility order satisfies the properties introduced in [6] as part of a new definition of perfect Bayesian equilibrium for dynamic games. Thus the present paper provides epistemic foundations for that solution concept. (shrink)

This paper contributes to the understanding of economic strategic behaviors in inter-temporal settings. Comparing the MPE and the OLNE of a widely used class of differential games it is shown: (i) what qualifications on behaviors a markov (dynamic) information structure brings about compared with an open-loop (static) information structure, (ii) what is the reason leading to intensified or reduced competition between the agents in the long run. It depends on whether agents’ interactions are characterized by markov substitutability or markov complementarity, (...) which can be seen as dynamic translations of the ideas of strategic substitutability and strategic complementarity (Bulow et al. 1985, Journal of Political Economy 93:488–511). In addition, an important practical contribution of the paper for modelers is to show that these results can be directly deduced from the payoff structure, with no need to compute equilibria first. (shrink)

Brian Skyrms constructs a theory of "dynamic deliberation" and uses it to investigate rational decision-making in cases of strategic interaction. This illuminating book will be of great interest to all those in many disciplines who use decision theory and game theory to study human behavior and thought. Skyrms begins by discussing the Bayesian theory of individual rational decision and the classical theory of games, which at first glance seem antithetical in the criteria used for determining action. In his effort (...) to show how methods for dealing with information feedback can be productively combined, the author skillfully leads us through the mazes of equilibrium selection, the Nash equilibria for normal and extensive forms, structural stability, causal decision theory, dynamic probability, the revision of beliefs, and, finally, good habits for decision. The author provides many clarifying illustrations and a handy appendix called "Deliberational Dynamics on Your Personal Computer." His powerful model has important implications for understanding the rational origins of convention and the social contract, the logic of nuclear deterrence, the theory of good habits, and the varied strategies of political and economic behavior. (shrink)

Stakeholder literature has acknowledged the need to complement the extant theory on stakeholder management by more dynamic perspectives. This article makes use of the recent terminology of stakewatcher and stakeseeker to illustrate the dynamic aspect of stakeholder theory transposed in the graphical representation of Freeman’s stakeholder model. Presenting a few selected case studies, it applies the scheme on the concept of value responsibility chain; it exemplifies the role of stakeseekers in various forms of activism, from shareholders, NGOs and government, in (...) the stakeholder mobilisation process. This article clarifies how stakewatchers and stakeseekers can profoundly affect stakeholder salience, especially in crises. The transposition and integration of the dynamic aspect of stakeholder theory into the graphical representation strengthen the forceful pedagogical value of the Freeman’s stakeholder graphical model. (shrink)

Animal welfare in livestock farming is a general concept that involves many concrete ethical issues for which solutions need to be developed. To avoid disturbing the internal market, the European Union encourages market players to develop harmonized solutions to such issues. One issue is the castration of piglets without pain relief, the practice of which causes pain to piglets. Although scientists have found alternatives to replace castration without pain relief, the process of solving the castration issue has stagnated. Questions remain (...) as to why this painful castration practice has still not been addressed after three decades, how it is likely to develop in the near future, and whether it will lead to a single harmonized solution for the EU. To answer these questions, this study examines the development of the castration issue using in-depth interviews and desk research. The results show that different countries have developed different solutions at different stages of the issue’s development. For a long period, the developments did not set a course toward a single solution; most EU pork producers waited for a castration ban in Germany. Such a situation was turbulent in solving the issue because the heterogeneous EU was unlikely to agree upon on a single alternative. With the EU now taking a market-based orientation, however, solving the issue now seems more likely. More attention is needed to understand market opportunities and chain integration in this area. (shrink)

In this paper I will discuss the problem of evaluating dynamic properties of the procedural rules that govern science. I will propose a novel framework for evaluating dynamic properties of such rules. This framework is based upon an analogy from New Institutional Economics. I will argue that the concept of ‘adaptive efficiency’, as it has been developed by Douglass North, solves a problem in economics that is analogous to the problem of evaluating dynamic properties of the procedural rules that govern (...) science. I will propose to apply the main ideas underlying this concept to Chrysostomos Mantzavinos’s theory of Explanatory Games. Based on these ideas, I will develop the concept of ‘explanatory efficiency’. This concept is meant to provide the means to evaluate the dynamic properties of Explanatory Games. I will argue that the proposed analogy also motivates more general applications of New Institutional Economics to traditional problems of philosophy of science. (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)