Search Results (13)

This study introduces a simple model, which can be used to examine the influence of reputation on expected income achieved within the Iterated Prisoner’s Dilemma (IPD) game framework. The research explores how different reputation distributions among society members impact overall outcomes by modeling a society of agents, each characterized by a reputation score that dictates their likelihood of cooperation. Due to the simplicity of the model, we can analytically determine the expected incomes based on the distribution of agents’ reputations and model parameters. The results show that a higher reputation generally leads to greater expected income, thereby promoting cooperation over defection. However, in some cases, where there are more defecting individuals, the expected income reaches the maximum for agents with an average reputation, and then decreases for individuals who cooperate more. Various scenarios, including uniform, increasing, and decreasing reputation distributions, are analyzed to understand their effects on the promoted interaction strategy. Finally, we outline future extensions of the model and potential research directions, including the exploration of alternative reputation distributions, variable interaction parameters, and different payoff structures in the dilemma games. Full article

In this paper, we focus on developing self-organizing algorithms aimed at solving, in a distributed way, the coverage problem in Wireless Sensor Networks (WSNs). For this purpose, we apply a game-theoretical framework based on an application of a variant of the Spatial Prisoner’s Dilemma game. The framework is used to build a multi-agent system, where agent-players in the process of iterated games tend to achieve a Nash equilibrium, providing them the possible maximal values of payoffs. A reached equilibrium corresponds to a global solution for the coverage problem represented by the following two objectives: coverage and the corresponding number of sensors that need to be turned on. A multi-agent system using the game-theoretic framework assumes the creation of a graph model of WSNs and the further interpretation of nodes of the WSN graph as agents participating in iterated games. We use the following two types of reinforcement learning machines as agents: Learning Automata (LA) and Cellular Automata (CA). The main novelty of the paper is the development of a specialized reinforcement learning machine based on the application of ($ϵ,h$)-learning automata. As the second model of an agent, we use the adaptive CA that we recently proposed. While both agent models operate in discrete time, they differ in the way they store and use available information. LA-based agents store in their memories the current information obtained in the last h-time steps and only use this information to make a decision in the next time step. CA-based agents only retain information from the last time step. To make a decision in the next time step, they participate in local evolutionary competitions that determine their subsequent actions. We show that agent-players reaching the Nash equilibria corresponds to the system achieving a global optimization criterion related to the coverage problem, in a fully distributed way, without the agents’ knowledge of the global optimization criterion and without any central coordinator. We perform an extensive experimental study of both models and show that the proposed learning automata-based model significantly outperforms the cellular automata-based model. Full article

Living organisms expend energy to sustain survival, a process which is reliant on consuming resources—termed here as the “cost of survival”. In the Prisoner’s Dilemma (PD), a classic model of social interaction, individual payoffs depend on choices to either provide benefits to others at a personal cost (cooperate) or exploit others to maximize personal gain (defect). We demonstrate that in an iterated Prisoner’s Dilemma (IPD), a simple “Always Cooperate” (ALLC) strategy evolves and remains evolutionarily stable when the cost of survival is sufficiently high, meaning exploited cooperators have a low probability of survival. We derive a rule for the evolutionary stability of cooperation, x/z >T/R, where x represents the duration of mutual cooperation, z the duration of exploitation, T the defector’s free-riding payoff, and R the payoff for mutual cooperation. This finding suggests that higher survival costs can enhance social welfare by selecting for cooperative strategies. Full article

The global geopolitical landscape is characterized by the rise of new powers and a shift toward multipolarity. This study examines the impact of multipolarity on international cooperation using an iterated game theory approach, particularly the classic prisoner’s dilemma, extended to a multiplayer setting. This effort can be regarded as a preliminary study of hypothetical optimal global cooperation. The main hypothesis is that an increase in the number of large countries in the international system will lead to higher levels of cooperation. Our simulation approach confirmed this. Our findings extend to the conclusion that multipolarity, under appropriate cultural and value systems, can foster new economic development and fair competition. Furthermore, we emphasize the importance of evolving strategies and cooperative dynamics in a multipolar world, contributing to discussions on foreign economic policy integration, sustainability, and managing vulnerabilities among great powers. The study underscores the necessity of strategic frameworks and international institutions in promoting global stability and cooperation amidst the complexities of multipolarity. Full article

We formulate and study a two-player duel game as a terminal payoffs stochastic game. Players $P_1,P_2$ are standing in place and, in every turn, each may shoot at the other (in other words, abstention is allowed). If $P_n$ shoots $P_m$ ($m\ne n$), either they hit and kill them (with probability $p_n$) or they miss and $P_m$ is unaffected (with probability $1-p_n$). The process continues until at least one player dies; if no player ever dies, the game lasts an infinite number of turns. Each player receives a positive payoff upon killing their opponent and a negative payoff upon being killed. We show that the unique stationary equilibrium is for both players to always shoot at each other. In addition, we show that the game also possesses “cooperative” (i.e., non-shooting) non-stationary equilibria. We also discuss a certain similarity that the duel has to the iterated Prisoner’s Dilemma. Full article

We propose an approach to self-optimizing wireless sensor networks (WSNs) which are able to find, in a fully distributed way, a solution to a coverage and lifetime optimization problem. The proposed approach is based on three components: (a) a multi-agent, social-like interpreted system, where the modeling of agents, discrete space, and time is provided by a 2-dimensional second-order cellular automata, (b) the interaction between agents is described in terms of the spatial prisoner’s dilemma game, and (c) a local evolutionary mechanism of competition between agents exists. Nodes of a WSN graph created for a given deployment of WSN in the monitored area are considered agents of a multi-agent system that collectively make decisions to turn on or turn off their batteries. Agents are controlled by cellular automata (CA)-based players participating in a variant of the spatial prisoner’s dilemma iterated game. We propose for players participating in this game a local payoff function that incorporates issues of area coverage and sensors energy spending. Rewards obtained by agent players depend not only on their personal decisions but also on their neighbor’s decisions. Agents act in such a way to maximize their own rewards, which results in achieving by them a solution corresponding to the Nash equilibrium point. We show that the system is self-optimizing, i.e., can optimize in a distributed way global criteria related to WSN and not known for agents, provide a balance between requested coverage and spending energy, and result in expanding the WSN lifetime. The solutions proposed by the multi-agent system fulfill the Pareto optimality principles, and the desired quality of solutions can be controlled by user-defined parameters. The proposed approach is validated by a number of experimental results. Full article

One of the leading theories for the origin of life includes the hypothesis according to which life would have evolved as cooperative networks of molecules. Explaining cooperation—and particularly, its emergence in favoring the evolution of life-bearing molecules—is thus a key element in describing the transition from nonlife to life. Using agent-based modeling of the iterated prisoner’s dilemma, we investigate the emergence of cooperative behavior in a stochastic and spatially extended setting and characterize the effects of inheritance and variability. We demonstrate that there is a mutation threshold above which cooperation is—counterintuitively—selected, which drives a dramatic and robust cooperative takeover of the whole system sustained consistently up to the error catastrophe, in a manner reminiscent of typical phase transition phenomena in statistical physics. Moreover, our results also imply that one of the simplest conditional cooperative strategies, “Tit-for-Tat”, plays a key role in the emergence of cooperative behavior required for the origin of life. Full article

In the much-studied Centipede Game, which resembles the Iterated Prisoners’ Dilemma, two players successively choose between (1) cooperating, by continuing play, or (2) defecting and terminating play. The subgame-perfect Nash equilibrium implies that play terminates on the first move, even though continuing play can benefit both players—but not if the rival defects immediately, which it has an incentive to do. We show that, without changing the structure of the game, interchanging the payoffs of the two players provides each with an incentive to cooperate whenever its turn comes up. The Nash equilibrium in the transformed Centipede Game, called the Reciprocity Game, is unique—unlike the Centipede Game, wherein there are several Nash equilibria. The Reciprocity Game can be implemented noncooperatively by adding, at the start of the Centipede Game, a move to exchange payoffs, which it is rational for the players to choose. What this interchange signifies, and its application to transforming an arms race into an arms-control treaty, are discussed. Full article

In this work, we explore the role of learning dynamics and social norms in human cooperation on networks. We study the model recently introduced in [Physical Review E, 97, 042321 (2018)] that integrates the well-studied Experience Weighted Attraction learning model with some features characterizing human norm psychology, namely the set of cognitive abilities humans have evolved to deal with social norms. We provide further evidence that this extended model—that we refer to as Experience Weighted Attraction with Norm Psychology—closely reproduces cooperative patterns of behavior observed in large-scale experiments with humans. In particular, we provide additional support for the finding that, when deciding to cooperate, humans balance between the choice that returns higher payoffs with the choice in agreement with social norms. In our experiment, agents play a prisoner’s dilemma game on various network structures: (i) a static lattice where agents have a fixed position; (ii) a regular random network where agents have a fixed position; and (iii) a dynamic lattice where agents are randomly re-positioned at each game iteration. Our results show that the network structure does not affect the dynamics of cooperation, which corroborates results of prior laboratory experiments. However, the network structure does seem to affect how individuals balance between their self-interested and normative choices. Full article

Iterated games, in which the same economic interaction is repeatedly played between the same agents, are an important framework for understanding the effectiveness of strategic choices over time. To date, very little work has applied information theory to the information sets used by agents in order to decide what action to take next in such strategic situations. This article looks at the mutual information between previous game states and an agent’s next action by introducing two new classes of games: “invertible games” and “cyclical games”. By explicitly expanding out the mutual information between past states and the next action we show under what circumstances the explicit values of the utility are irrelevant for iterated games and this is then related to revealed preferences theory of classical economics. These information measures are then applied to the Traveler’s Dilemma game and the Prisoner’s Dilemma game, the Prisoner’s Dilemma being invertible, to illustrate their use. In the Prisoner’s Dilemma, a novel connection is made between the computational principles of logic gates and both the structure of games and the agents’ decision strategies. This approach is applied to the cyclical game Matching Pennies to analyse the foundations of a behavioural ambiguity between two well studied strategies: “Tit-for-Tat” and “Win-Stay, Lose-Switch”. Full article

For the iterated Prisoner’s Dilemma there exist good strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent’s payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long term payoff, these strategies effectively stabilize cooperative behavior. The existence of such strategies follows from the so-called Folk Theorem for supergames, and the proof constructs an explicit memory-one example, which has been labeled Grim. Here we describe all the memory-one good strategies for the non-symmetric version of the Prisoner’s Dilemma. This is the natural object of study when the payoffs are in units of the separate players’ utilities. We discuss the special advantages and problems associated with some specific good strategies. Full article

We use an agent-based model to investigate the interdependent dynamics between individual agency and emergent socioeconomic structure, leading to institutional change in a generic way. Our model simulates the emergence and exit of institutional units, understood as generic governed social structures. We show how endogenized trust and exogenously given leader authority influences institutional change, i.e., diversity in institutional life-cycles. It turns out that these governed institutions (de)structure in cyclical patterns dependent on the overall evolution of trust in the artificial society, while at the same time, influencing this evolution by supporting social learning. Simulation results indicate three scenarios of institutional life-cycles. Institutions may, (1) build up very fast and freeze the artificial society in a stable but fearful pattern (ordered system); (2) exist only for a short time, leading to a very trusty society (highly fluctuating system); and (3) structure in cyclical patterns over time and support social learning due to cumulative causation of societal trust (complex system). Full article

The finitely repeated Prisoners’ Dilemma is a good illustration of the discrepancy between the strategic behaviour suggested by a game-theoretic analysis and the behaviour often observed among human players, where cooperation is maintained through most of the game. A game-theoretic reasoning based on backward induction eliminates strategies step by step until defection from the first round is the only remaining choice, reflecting the Nash equilibrium of the game. We investigate the Nash equilibrium solution for two different sets of strategies in an evolutionary context, using replicator-mutation dynamics. The first set consists of conditional cooperators, up to a certain round, while the second set in addition to these contains two strategy types that react differently on the first round action: The ”Convincer” strategies insist with two rounds of initial cooperation, trying to establish more cooperative play in the game, while the ”Follower” strategies, although being first round defectors, have the capability to respond to an invite in the first round. For both of these strategy sets, iterated elimination of strategies shows that the only Nash equilibria are given by defection from the first round. We show that the evolutionary dynamics of the first set is always characterised by a stable fixed point, corresponding to the Nash equilibrium, if the mutation rate is sufficiently small (but still positive). The second strategy set is numerically investigated, and we find that there are regions of parameter space where fixed points become unstable and the dynamics exhibits cycles of different strategy compositions. The results indicate that, even in the limit of very small mutation rate, the replicator-mutation dynamics does not necessarily bring the system with Convincers and Followers to the fixed point corresponding to the Nash equilibrium of the game. We also perform a detailed analysis of how the evolutionary behaviour depends on payoffs, game length, and mutation rate. Full article