Showing papers on "Stochastic game published in 1993"
TL;DR: In this paper, the authors extend evolutionary game theory to include spatial dimensions, and find that spatial effects can change the outcome of frequency dependent selection and that strategies may coexist that would not coexist in homogeneous populations.
Abstract: Evolutionary game theory can be extended to include spatial dimensions. The individual players are placed in a two-dimensional spatial array. In each round every individual “plays the game” with its immediate neighbours. After this, each site is occupied by its original owner or by one of the neighbours, depending on who scored the highest payoff. These rules specify a deterministic cellular automaton. We find that spatial effects can change the outcome of frequency dependent selection. Strategies may coexist that would not coexist in homogeneous populations. Spatial games have interesting mathematical properties. There are static or chaotically changing patterns. For symmetrical starting conditions we find “dynamical fractals” and “evolutionary kaleidoscopes.” There is a new world to be explored.
673 citations
TL;DR: In this paper, it is shown that players who know their own payoff matrices and choose strategies to maximize their expected utility, must eventually play according to a Nash equilibrium of the repeated game.
Abstract: Each of n players, in an infinitely repeated game, starts with subjective beliefs about his opponents' strategies. If the individual beliefs are compatible with the true strategies chosen, then Bayesian updating will lead in the long run to accurate prediction of the future play of the game. It follows that individual players, who know their own payoff matrices and choose strategies to maximize their expected utility, must eventually play according to a Nash equilibrium of the repeated game. An immediate corollary is that, when playing a Harsanyi-Nash equilibrium of a repeated game of incomplete information about opponents' payoff matrices, players will eventually play a Nash equilibrium of the real game, as if they had complete information.
592 citations
TL;DR: In this paper, the authors explore a sequential offers model of n-person coalitional bargaining with transferable utility and with time discounting, and focus on the efficiency properties of stationary equilibria of strictly superadditive games when the discount factor 'delta' is sufficiently large.
Abstract: The authors explore a sequential offers model of n-person coalitional bargaining with transferable utility and with time discounting. Their focus is on the efficiency properties of stationary equilibria of strictly superadditive games when the discount factor 'delta' is sufficiently large. It is shown that delay and the formation of inefficient subcoalitions can occur in equilibrium, the latter for some or all orders of proposer. However, efficient stationary equilibrium payoffs converge to a point in the core as 'delta' approaches one. Strict convexity is a sufficient condition for there to exist an efficient stationary equilibrium payoff vector for sufficiently high 'delta'.
327 citations
TL;DR: In this article, a nonlinear arbitrage-pricing model, a conditional linear model, and an unconditional linear model are used to price international equities, bonds, and forward currency contracts.
Abstract: This paper uses a nonlinear arbitrage-pricing model, a conditional linear model, and an unconditional linear model to price international equities, bonds, and forward currency contracts. Unlike linear models, the nonlinear arbitrage-pricing model requires no restrictions on the payoff space, allowing it to price payoffs of options, forward contracts, and other derivative securities. Only the nonlinear arbitragepricing model does an adequate job of explaining the time series behavior of a cross section of international returns. THE IDEA THAT A few relevant state variables explain expected returns is the main driving force of the seminal papers of Merton (1973) and Ross (1976). These seminal ideas have been extended to the pricing of international assets by Ikeda (1991), Ross and Walsh (1983), Solnik (1974, 1983), and Stulz (1981), among others.' The key implication of these arbitrage-pricing models is that only risks related to these factors (state variables) are relevant in determining asset prices. Testable implications of these international asset-pricing models have been derived either by placing restrictions on the payoff structure (i.e., payoffs are linear in factors) as in Ikeda (1991), Ross and Walsh (1983), and Solnik (1983), or on the joint distributions of the payoffs and state variables as in Constantinides (1989). These restrictions lead to the testable implication that expected asset returns are linear in the conditional covariances with the factor payoffs. In what follows, we refer to these models as linear arbitrage models or linear models.
199 citations
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TL;DR: This paper provided experimental evidence on forward induction as a refinement criterion and found only limited support for the forward induction hypothesis, and the effects of the outside option also reflected the creation of a focal point through the asymmetry created by offering the outside options to one of the two players.
Abstract: This paper provides experimental evidence on forward induction as a refinement criterion. In the basic extensive form, one of the two players chooses to play a battle-of-the-sexes game or to receive a certain payoff. According to forward induction, choosing to play the game is a signal about intended action. Though the presence of the outside option changes play, we find only limited support for the forward-induction hypothesis. The effects of the outside option also reflect the creation of a focal point through the asymmetry created by offering the outside option to one of the two players. (JEL C72)
154 citations
TL;DR: The generalized asymmetric VOD is similar to market entry games in the sense that the interest in the collective good and/or the production costs (i.e. work) may vary between actors.
Abstract: The symmetric Volunteer’s dilemma game (VOD) models a situation in which each of N actors faces the decision of either producing a step-level collective good (action “C”) or freeriding (“D”). One player’s cooperative action suffices for producing the collective good. Unilateral cooperation yields a payoff U for D-players and U - K for the cooperative player(s). However, if all actors decide for “freeriding”, each player’s payoff is zero (U > K > 0). In this article, an essential modification is discussed. In an asymmetric VOD, the interest in the collective good and/or the production costs (i.e. work) may vary between actors. The generalized asymmetric VOD is similar to market entry games. Alternative hypotheses abaout the behavior of subjects are derived from a game-theoretical analysis. They are investigated in an experimental setting. The application of the mixed Nash-equilibrium concept yields a rather counter-intuitive prediction which apparently contradicts the empirical data. The predictions of the Harsanyi-Selten-theory and Schelling’s “focal point theory” are in better accordance with the data. However, they do not account for the “diffusion-of-responsibility-effect” also observable in the context of an asymmetric VOD game.
115 citations
TL;DR: In this article, the authors developed a model of strategic behavior in continuous time games of complete information, which includes conventional repeated games in discrete time as a special case, and applied these results to a Cournot duopoly example.
Abstract: In this paper, the authors develop a model of strategic behavior in continuous time games of complete information, which includes conventional repeated games in discrete time as a special case. The model developed here admits a very large class of strategies that allows one to extend the repeated game model to continuous time. The set of equilibria in this game may be large--in many cases equal to the feasible individually rational set of payoff s. The authors also study the restriction of renegotiation proofness in this framework and apply these results to a Cournot duopoly example. Copyright 1993 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.
101 citations
TL;DR: For games with incomplete information, this article showed that player one will get a t least her commitment payoff in any Nash equilibrium of the repeated game if her discount factor approaches one, and this result is robust against further perturbations of the informational structure.
Abstract: A two-person game is of conflicting interests if the strategy to which player one would most like to commit herself holds player two down to his minimax payoff. Suppose there is a positive prior probability that player one is a "commitme nt type" who will always play this strategy. Then player one will get a t least her commitment payoff in any Nash equilibrium of the repeated game if her discount factor approaches one. This result is robust against further perturbations of the informational structure and in striking contrast to the message of the Folk theorem for games with incomplete information. Copyright 1993 by The Econometric Society.
81 citations
TL;DR: In this article, the authors considered two-person zero-sum stochastic games with limit superior payoff function and Borel measurable state and action spaces and proved the games are upper analytic.
Abstract: We consider two-person zero-sum stochastic games with limit superior payoff function and Borel measurable state and action spaces. The games are shown to have a value and the value function is calculated by transfinite iteration of an operator and proved to be upper analytic. The paper extends results of our earlier article [17] in which the same class of games was considered for countable state spaces and finite action sets.
70 citations
TL;DR: In this paper, it was shown that if the stage game is an extensive game with perfect information, any Nash equilibrium of the machine game will induce a path consisting of a constant play of a Nash equilibrium for the stage-game.
64 citations
TL;DR: In this article, an extension of Dixit and Shapiro's model of uncoordinated entry dynamics to the case when there are experience advantages is proposed. But the model assumes that each firm's payoff from being in the market increases with past experience, measured by the number of periods it has previously been active.
TL;DR: In this article, the authors analyse anti-pollution policies in a 2-by-2 game played between a "polluter" and the "police" in which the payoffs can be manipulated by an exogenous third player called the policymaker.
Abstract: In this paper we analyse anti-pollution policies in a 2-by-2 game played between a “polluter” and the “police” in which the payoffs can be manipulated by an exogenous third player called the “policy-maker.” We show that the efficiency of the policies may depend on whether the players of the 2-by-2 game choose Nash equilibrium strategies or prefer maximin.
TL;DR: A decision maker is facing a dynamic system which is being controlled by himself/herself as well as by other decision makers, and whether this decision maker can guarantee a performance vector which approaches this desired set is considered for the worst-case scenario.
Abstract: A decision maker is facing a dynamic system which is being controlled by himself/herself as well as by other decision makers. He/she considers a vector of performance measures. Acceptable performance is defined through a set in the space of performance vectors. Whether this decision maker can guarantee a (time-averaged) performance vector which approaches this desired set is considered for the worst-case scenario, in which other decision makers may, for selfish reasons, try to exclude his/her vector from the desired set. For a controlled Markov model of the system, a sufficient condition for approachability is given, and appropriate control strategies are constructed. Under certain recurrence conditions, a complete characterization of approachability is then provided for convex sets. The mathematical formulation leads to a theory of approachability for stochastic games with vector payoffs. A simple queuing example illustrates this approach. >
TL;DR: It is shown that any Nash equilibrium point of this bimatrix game can be used to find a Nash equilibriumpoint of the stochastic game whenever the law of motion is controlled by one player.
Abstract: Given a non-zero sum discounted stochastic game with finitely many states and actions one can form a bimatrix game whose pure strategies are the pure stationary strategies of the players and whose penalty payoffs consist of the total discounted costs over all states at any pure stationary pair. It is shown that any Nash equilibrium point of this bimatrix game can be used to find a Nash equilibrium point of the stochastic game whenever the law of motion is controlled by one player. The theorem is extended to undiscounted stochastic games with irreducible transitions when the law of motion is controlled by one player. Examples are worked out to illustrate the algorithm proposed.
TL;DR: In this paper, the existence of an equilibrium in stationary strategies for two-player zero-sum games with countable state space, compact action spaces, and limiting average payoff was established under a certain Liapunov stability condition.
Abstract: We study stochastic games with countable state space, compact action spaces, and limiting average payoff. ForN-person games, the existence of an equilibrium in stationary strategies is established under a certain Liapunov stability condition. For two-person zero-sum games, the existence of a value and optimal strategies for both players are established under the same stability condition.
TL;DR: In this article, it is shown that for every NTU market game and for any point in its inner core, there is a market that represents the game and further has the given inner core point as its unique competitive payoff vector.
Abstract: It is shown that for every NTUmarket game, there is amarket thatrepresents the game whosecompetitive payoff vectors completely fill up theinner core of the game. It is also shown that for every NTU market game and for any point in its inner core, there is a market that represents the game and further has the given inner core point as itsunique competitive payoff vector. These results prove a conjecture of Shapley and Shubik.Journal of Economic Literature Classification Numbers: C71, D51.
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01 Jan 1993TL;DR: In this article, the authors extend the traditional iterated prisoner's dilemma (IPD) with round-robin partner matching by permitting players to choose and refuse partners in each iteration on the basis of continually updated expected payoffs.
Abstract: This article extends the traditional iterated prisoner's dilemma (IPD) with round-robin partner matching by permitting players to choose and refuse partners in each iteration on the basis of continually updated expected payoffs. Comparative computer experiments are reported that indicate the introduction of partner choice and refusal accelerates the emergence of mutual cooperation in the IPD relative to round-robin partner matching. Moreover, in contrast to findings for round-robin partner matching (in which the average payoffs of the players tend to be either clustered around the mutual cooperation payoff or widely scattered), the average payoff scores of the players with choice and refusal of partners tend to cluster into two or more distinct narrow bands. Preliminary analytical and computational sensitivity studies are also reported for several key parameters. Related work can be accessed here: http://www2.econ.iastate.edu/tesfatsi/tnghome.htm
01 Jun 1993
TL;DR: This paper introduces an efficient and fair allocation rule which selects a payoff for every possible situation with incompatibilities (when the set of players is fixed), and proves that it is uniquely determined.
Abstract: A situation with incompatibilities is defined to be a TU-game together with a graph whose arcs link pairs of incompatible players. In this paper we introduce an efficient and fair allocation rule which selects a payoff for every possible situation with incompatibilities (when the set of players is fixed), and prove that it is uniquely determined. Besides, we demonstrate that it is stable, study its relationship with the so-calledIR-Shapley value and show that it generalizes an earlier theory for simple games. Finally, the communication situations with incompatibilities are studied.
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TL;DR: In this paper, the authors characterize the set of strategies that are stable with respect to a stochastic dynamic adaptive process in a finite two-player game played by a population of players.
Abstract: We add a round of pre-play communication to a finite two-player game played by a population of players. Pre-play communication is cheap talk in the sense that it does not directly enter the payoffs. The paper characterizes the set of strategies that are stable with respect to a stochastic dynamic adaptive process. Periodically players have an opportunity to change their strategy with a strategy that is more successful against the current population. Any strategy that weakly improves upon the current poorest performer in the population enters with positive probability. When there is no conflict of interest between the players, only the efficient outcome is stable with respect to these dynamics. For general games the set of stable payoffs is typically large. Every efficient payoff recurs infinitely often. Copyright 1995 by The Econometric Society.(This abstract was borrowed from another version of this item.)
TL;DR: In this article, the payoff function of Player 1 is convex or concave in the first variable, and it is shown that this assumption together with the boundedness of payoff functions imply the existence of Nash equilibria consisting of two probability measures concentrated at most at two points each.
Abstract: The paper investigates two classes of non-zero-sum two-person games on the unit square, where the payoff function of Player 1 is convex or concave in the first variable. It is shown that this assumption together with the boundedness of payoff functions imply the existence of ɛ-Nash equilibria consisting of two probability measures concentrated at most at two points each.
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TL;DR: It is shown that the relative interior of the core of a game with side payments is contained in the partnered core of the game if it is partnered, feasible and cannot be improved upon by any coalition of players.
Abstract: An outcome of a game is partnered if there are no asymmetric dependencies between any two players. For a cooperative game, a payoff is in the partnered core of the game if it is partnered, feasible and cannot be improved upon by any coalition of players. We show that the relative interior of the core of a game with side payments is contained in the partnered core. For quasi-strictly convex games the partnered core coincides with the relative interior of the core. When there are no more than three partnerships, the sums of the payoffs to partnerships are constant across all core payoffs. When there are no more than three players, the partnered core satisfies additional properties.
TL;DR: In this article, the authors give a characterization of equilibrium payoffs of a repeated game in which players use the long-run average of the one-shot game payoffs as the overall payoff of the repeated game and individual actions are not discernible by others.
TL;DR: In this article, a game situation is considered in which the players are two points of a manifold with a non-degenerate metric, each with controllable velocity, and the payoff in the game is the minimum distance between the players in a semi-infinite interval of the time of motion.
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TL;DR: The extent to which an uncommitted or normal type of patient player can exploit his less patient opponent's uncertainty to maintain a reputation for playing like a commitment type is investigated.
Abstract: We analyze in a game between a patient player 1 and a non-myopic but less patient opponent, player 2. We assume that Player 1's type is private information and that players do not directly observe each other's action but rather see an imperfect signal of it. We show that in any Nash equilibrium of the game player 1 will get almost the largest payoff consistent with player 2 choosing a best response in a finite truncation of the game. If the discount factor of player 2 is sufficiently large, then player 1 will get approximately the maximum payoff consistent with player 2 getting at least his pure strategy minmax payoff.
TL;DR: The paper shows that deterministic graphical games have a solution even when the graph has an infinite number of nodes.
Abstract: A deterministic graphical game is a two-person zero-sum game with perfect information played on a directed graph. Nodes with no successor are called terminal nodes and have a payoff associated with them. The other nodes are labelled to indicate which of the players chooses the successor node. Play starts at a specific node and only stops when a terminal node is reached at which point player 1 obtains the payoff corresponding to that node; if play never ends the payoff is zero. The paper shows that such games have a solution even when the graph has an infinite number of nodes.
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TL;DR: In this article, equilibrium binding agreements, the coalition structures that form under such agreements, and the efficiency of the outcomes that result are analyzed in a context where the payoff to each player depends on the actions of all other players.
Abstract: We study equilibrium binding agreements, the coalition structures that form under such agreements, and the efficiency of the outcomes that result. We analyze such agreements in a context where the payoff to each player depends on the actions of all other players. Thus a game in strategic form is a natural starting point. Unlike the device of a characteristic function, explicit attention is paid to the behavior of the complementary set of players when a coalition blocks a proposed agreement. A solution concept and its applications are discussed. Journal of Economic Literature Classification Numbers: C70, C71.
TL;DR: In this article, the existence of equilibrium payoffs in stochastic games with at most 3 states is proved in a new way, which implies that the game is solvable.
Abstract: This paper deals with undiscounted stochastic games. As in Thuijsman-Vrieze [9], we consider specific states, which we call solvable. The existence of such states in every game is proved in a new way. This proof implies the existence of equilibrium payoffs in stochastic games with at most 3 states. On an example, we relate our work to the construction of Thuijsman and Vrieze.
TL;DR: For non-zero-sum differential games with the open-loop information pattern, this paper showed that all games under consideration possess correlated ϵ-equilibria for any ϵ > 0.
TL;DR: In this article, the authors report results of experiments on three-person quota games without the grand coalition and with zero values for the one-person coalitions and the experimental procedure used is the demand commitment model, which generates finite extensive games with perfect information whose neutral equilibrium point predicts quota agreements.
Abstract: The paper reports results of experiments on three-person quota games without the grand coalition and with zero values for the one-person coalitions. The experimental procedure used is the demand commitment model. This model generates finite extensive games with perfect information whose neutral equilibrium point predicts quota agreements. The termneutral means that at every decision point all locally optimal choices are taken with equal probability. Quota agreements do not perform better than equal division payoff bounds, but nevertheless the experiments show that quotas have some behavioral relevance. The demand commitment model seems to favor learning of the quota concept if subjects have the opportunity to gain experience by frequently playing the same game.
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