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Evolutionary game theory is a basis of replicator systems and has applications ranging from animal behavior and human language to ecosystems and other hierarchical network systems. Most studies in evolutionary game dynamics have f...
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Evolutionary game theory is a basis of replicator systems and has applications ranging from animal behavior and human language to ecosystems and other hierarchical network systems. Most studies in evolutionary game dynamics have focused on a single game, but, in many situations, we see that many games are played simultaneously. We construct a replicator equation with plural games by assuming that a reward of a player is a simple summation of the reward of each game. Even if the numbers of the strategies of the games are different, its dynamics can be described in one replicator equation. We here show that when players play several games at the same time, the fate of a single game cannot be determined without knowing the structures of the whole other games. The most absorbing fact is that even if a single game has a ESS (evolutionary stable strategy), the relative frequencies of strategies in the game does not always converge to the ESS point when other games are played simultaneously. (c) 2006 Elsevier Ltd. All rights reserved.
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Dynamic (or stochastic) games are, in general, considerably more complicated to analyze than repeated games. This paper shows that for every deterministic dynamic game that is linear in the state, there exists a strategically equi...
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Dynamic (or stochastic) games are, in general, considerably more complicated to analyze than repeated games. This paper shows that for every deterministic dynamic game that is linear in the state, there exists a strategically equivalent representation as a repeated game. A dynamic game is said to be linear in the state if it holds for both the state transition function as well as for the one-period payoff function that (ⅰ) they are additively separable in action profiles and states and (ⅱ) the state variables enter linearly. Strategic equivalence refers to the observation that the two sets of subgame perfect equilibria coincide, up to a natural projection of dynamic game strategy profiles on the much smaller set of repeated game histories. Furthermore, it is shown that the strategic equivalence result still holds for certain stochastic elements in the transition function if one allows for additional signals in the repeated game or in the presence of a public correlating device.
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Real life is a bigger game in which what a player does early on can affect what others choose to do later on. In particular, we can strive to explain how cooperative behaviour can be established as a result of rational behaviour. ...
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Real life is a bigger game in which what a player does early on can affect what others choose to do later on. In particular, we can strive to explain how cooperative behaviour can be established as a result of rational behaviour. When engaged in a repeated situation, players must consider not only their short-term gains but also their long-term payoffs. The general idea of repeated games is that players may be able to deter another player from exploiting his short-term advantage by threatening a punishment that reduces his long-term payoff. The aim of the paper that supports this abstract is to present and discuss dynamic game theory. There are three basic kinds of reasons, which are not mutually exclusive, to study what happens in repeated games. First, it provides a pleasant and a very interesting theory and it has the advantage of making us become more humble in our predictions. Second, many of the most interesting economic interactions repeated often can incorporate a phenomenon which we believe are important but which are not captured when we restrict our attention to static games. Finally, economics, and equilibrium-based theories more generally, do best when analysing routinised interactions.
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In this work, we investigate consensus issues of discrete-time (DT) multi-agent systems (MASs) with completely unknown dynamic by using reinforcement learning (RL) technique. Different from policy iteration (PI) based algorithms t...
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In this work, we investigate consensus issues of discrete-time (DT) multi-agent systems (MASs) with completely unknown dynamic by using reinforcement learning (RL) technique. Different from policy iteration (PI) based algorithms that require admissible initial control policies, this work proposes a value iteration (VI) based model-free algorithm for consensus of DTMASs with optimal performance and no requirement of admissible initial control policy. Firstly, in order to utilize RL method, the consensus problem is modeled as an optimal control problem of tracking error system for each agent. Then, we introduce a VI algorithm for consensus of DTMASs and give a novel convergence analysis for this algorithm, which does not require admissible initial control input. To implement the proposed VI algorithm to achieve consensus of DTMASs without information of dynamics, we construct actor-critic networks to online estimate the value functions and optimal control inputs in real time. At last, we give some simulation results to show the validity of the proposed algorithm.& COPY; 2023 The Franklin Institute. Published by Elsevier Inc. All rights reserved.
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This paper addresses a problem with an argument in Kranich, Perea, and Peters [2005] supporting their definition of the Weak Sequential Core and their characterization result. We also provide the remedy, a modification of the defi...
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This paper addresses a problem with an argument in Kranich, Perea, and Peters [2005] supporting their definition of the Weak Sequential Core and their characterization result. We also provide the remedy, a modification of the definition, to rescue the characterization.
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Players A and B play a betting game. Player A starts with initial money n. In each of k rounds, player A can wager an integer w between 0 and what he has currently. B then decides whether A wins or loses. If A wins, he receives w ...
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Players A and B play a betting game. Player A starts with initial money n. In each of k rounds, player A can wager an integer w between 0 and what he has currently. B then decides whether A wins or loses. If A wins, he receives w money, and if A loses, he loses w money. A total of k rounds are played, but A can only lose r times. What strategy should A use to end with the maximum amount of money, D(n,k,r)? In this paper, we provide a strategy for A to maximize his money and the algorithm to calculate D(n,k, r). We study the periodicity of D(n+l, k, r) - D(n,k,r) relative to n. We will also extend n and w to non-negative real numbers. The maximum amount of money that A can obtain with continuous money is C(n, k, r), and we study the relationship between C and D.
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We consider a fc-player sequential bargaining model in which the size of the cake and the order in which players move follow a general Markov process. For games in which one agent makes an offer in each period and agreement must b...
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We consider a fc-player sequential bargaining model in which the size of the cake and the order in which players move follow a general Markov process. For games in which one agent makes an offer in each period and agreement must be unanimous, we characterize the sets of subgame perfect and stationary subgame perfect payoffs. With these character-izations, we investigate the uniqueness and efficiency of the equilibrium outcomes, the conditions under which agreement is delayed, and the advantage to proposing. Our analysis generalizes many existing results for games of sequential bargaining which build on the work of Stahl (1972), Rubinstein (1982), and Binmore (1987).
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This article studies the equilibrium states that can be reached in a network design game via natural game dynamics. First, we show that an arbitrarily interleaved sequence of arrivals and departures of players can lead to a polyno...
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This article studies the equilibrium states that can be reached in a network design game via natural game dynamics. First, we show that an arbitrarily interleaved sequence of arrivals and departures of players can lead to a polynomially inefficient solution at equilibrium. This implies that the central controller must have some control over the timing of agent arrivals and departures to ensure efficiency of the system at equilibrium. Indeed,we give a complementary result showing that if the central controller is allowed to restore equilibrium after every set of arrivals/departures via improving moves, then the eventual equilibrium states reached have exponentially better efficiency.
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This paper is concerned with the question of how to define the core when cooperation takes place in a dynamic setting. The focus is on dynamic cooperative games in which the players face a finite sequence of exogenously specified ...
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This paper is concerned with the question of how to define the core when cooperation takes place in a dynamic setting. The focus is on dynamic cooperative games in which the players face a finite sequence of exogenously specified TU-games. Three different core concepts are presented: the classical core, the strong sequential core and the weak sequential core. The differences between the concepts arise from different interpretations of profitable deviations by coalitions. Sufficient conditions are given for nonemptiness of the classical core in general and of the weak sequential core for the case of two players. Simplifying characterizations of the weak and strong sequential core are provided. Examples highlight the essential difference between these core concepts.
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I study a bilateral bargaining game in which the size of the surplus follows a stochastic process and in which players might be optimistic about their bargaining power. Following Yildiz (2003), I model optimism by assuming that pl...
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I study a bilateral bargaining game in which the size of the surplus follows a stochastic process and in which players might be optimistic about their bargaining power. Following Yildiz (2003), I model optimism by assuming that players have different beliefs about the recognition process. I show that the unique subgame perfect equilibrium of this game might involve inefficient delays. I also show that these inefficiencies disappear when players can make offers arbitrarily frequently.
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