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on Game Theory |
| By: | Takashi Kamihigashi (Research Institute for Economics and Business Administration, Kobe University); Taiji Furusawa (Graduate School of Economics, Hitotsubashi University) |
| Abstract: | This paper studies the global dynamics of a class of infinitely repeated two-player games in which the action space of each player is an interval, and the one-shot payoff of each player is additively separable in their actions. We define an immediately reactive equilibrium (IRE) as a pure-strategy subgame perfect equilibrium such that each player's action is a stationary function of the opponent's last action. We completely characterize IREs and their dynamics in terms of certain indifference curves. Our results are used to show that in a prisoners' dilemma game with observable mixed strategies, gradual cooperation occurs when the players are sufficiently patient, and that in a certain duopoly game, kinked demand curves emerge naturally. |
| Keywords: | Immediately reactive equilibria; additively separable payoffs; kinked demand; gradual cooperation; prisoners' dilemma |
| Date: | 2010–02 |
| URL: | http://d.repec.org/n?u=RePEc:kob:dpaper:dp2010-04&r=gth |
| By: | Kleppe, J. (Tilburg University) |
| Abstract: | This Ph. D. thesis deals with various topics within the field of game theory. The first chapters of the thesis focus on cooperative game theory, which mainly studies fair allocations of joint benefits by means of cooperation. In particular the per capita prenucleolus, public congestion network situations and cooperative situations are considered. Non-cooperative game theory studies situations in which players are unable to make binding agreements. Therefore, the focus is on individual incentives. The chapter on transfer equilibria and contract games forms a bridge between cooperative and non-cooperative game theory as we allow certain aspects of commitment and cooperation within the framework of non-cooperative games in strategic form. The final chapter of this thesis extensively studies fall back equilibrium. This equilibrium concept is a refinement of Nash equilibrium, which is the most fundamental solution concept in non-cooperative game theory. |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:ner:tilbur:urn:nbn:nl:ui:12-3763576&r=gth |
| By: | Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | In cooperative game theory, games in partition function form are real-valued function on the set of so-called embedded coalitions, that is, pairs $(S,\pi)$ where $S$ is a subset (coalition) of the set $N$ of players, and $\pi$ is a partition of $N$ containing $S$. Despite the fact that many studies have been devoted to such games, surprisingly nobody clearly defined a structure (i.e., an order) on embedded coalitions, resulting in scattered and divergent works, lacking unification and proper analysis. The aim of the paper is to fill this gap, thus to study the structure of embedded coalitions (called here embedded subsets), and the properties of games in partition function form. |
| Keywords: | Partition; Embedded subset; Game; Valuation; k-monotonicity |
| Date: | 2010–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:hal-00457827_v1&r=gth |
| By: | Béal, Sylvain; Rémila, Eric; Solal, Philippe |
| Abstract: | We consider an alternative expression of the Shapley value that reveals a system of compensations: each player receives an equal share of the worth of each coalition he belongs to, and has to compensate an equal share of the worth of any coalition he does not belong to. We give an interpretation in terms of formation of the grand coalition according to an ordering of the players and define the corresponding compensation vector. Then, we generalize this idea to cooperative games with a communication graph. Firstly, we consider cooperative games with a forest (cycle-free graph). We extend the compensation vector by considering all rooted spanning trees of the forest (see Demange 2004) instead of orderings of the players. The associated allocation rule, called the compensation solution, is characterized by component efficiency and relative fairness. The latter axiom takes into account the relative position of a player with respect to his component. Secondly, we consider cooperative games with arbitrary graphs and construct rooted spanning trees by using the classical algorithms DFS and BFS. If the graph is complete, we show that the compensation solutions associated with DFS and BFS coincide with the Shapley value and the equal surplus division respectively. |
| Keywords: | Shapley value ; compensations ; relative fairness ; compensation solution ; DFS ; BFS ; equal surplus division |
| JEL: | C71 |
| Date: | 2010–02–24 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:20955&r=gth |
| By: | Duersch, Peter; Oechssler, Joerg; Schipper, Burkhard C |
| Abstract: | It is well known that the rock-paper-scissors game has no pure saddle point. We show that this holds more generally: A symmetric two-player zero-sum game has a pure saddle point if and only if it is not a generalized rock-paper-scissors game. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure saddle point. Further sufficient conditions for existence are provided. We apply our theory to a rich collection of examples by noting that the class of symmetric two-player zero-sum games coincides with the class of relative payoff games associated with symmetric two-player games. This allows us to derive results on the existence of a finite population evolutionary stable strategies. |
| Keywords: | symmetric two-player games; zero-sum games; Rock-Paper-Scissors; single-peakedness; quasiconcavity; finite population evolutionary stable strategy; increasing differences; decreasing differences; potentials; additive separability |
| JEL: | C72 C73 |
| Date: | 2010–02–21 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:20864&r=gth |
| By: | Azar, Ofer H.; Bar-Eli, Michael |
| Abstract: | Mixed-strategy Nash equilibrium (MSNE) is a commonly-used solution concept in game-theoretic models in various fields in economics, management, and other disciplines, but the experimental results whether the MSNE predicts well actual play in games is mixed. Consequently, evidence for naturally-occurring games in which the MSNE predicts the outcome well is of great importance, as it can justify the vast use of MSNE in models. The game between the kicker and goalkeeper in soccer penalty kicks is a real-world game that can be used to examine the application of the MSNE concept or its accuracy because payoffs are a common knowledge, the players have huge incentives to play correctly, the game is simple enough to analyze, its Nash equilibrium is in mixed strategies, and players' actions can be observed. We collected and analyzed data on the direction of kicks and jumps in penalty kicks in various top leagues and tournaments. Our analysis suggests that the MSNE predictions are the closest to the actual sample data, even though some other prediction methods use information on the marginal distribution of kicks or jumps whereas the MSNE does not. |
| Keywords: | Soccer; Football; MSNE; Mixed-strategies; Mixed-strategy Nash equilibrium; Sports; Penalty kicks |
| JEL: | L83 C70 D00 C93 C72 |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:20964&r=gth |
| By: | Duersch, Peter; Oechssler, Joerg; Schipper, Burkhard C |
| Abstract: | We show that for many classes of symmetric two-player games, the simple decision rule "imitate-the-best" can hardly be beaten by any other decision rule. We provide necessary and sufficient conditions for imitation to be unbeatable and show that it can only be beaten by much in games that are of the rock-scissors-paper variety. Thus, in many interesting examples, like 2x2 games, Cournot duopoly, price competition, rent seeking, public goods games, common pool resource games, minimum effort coordination games, arms race, search, bargaining, etc., imitation cannot be beaten by much even by a very clever opponent. |
| Keywords: | Imitate-the-best; learning; symmetric games; relative payoffs; zero-sum games; rock-paper-scissors; finite population ESS; potential games; quasisubmodular games; quasisupermodular games; quasiconcave games; aggregative games |
| JEL: | D43 C73 C72 |
| Date: | 2010–02–18 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:20856&r=gth |
| By: | Bobtcheff, Catherine (Toulouse School of Economics (CNRS, LERNA)); Mariotti, Thomas (Toulouse School of Economics (CNRS, GREMAQ, IDEI)) |
| Abstract: | We consider a preemption game with two potential competitors who come into play at some random secret times. The presence of a competitor is revealed to a player only when the former moves, which terminates the game. We show that all perfect Bayesian equilibria give rise to the same distribution of players' moving times. Moreover, there exists a unique perfect Bayesian equilibrium in which each player's behavior from any time on is independent of the date at which she came into play. We find that competitive pressure is nonmonotonic over time, and that private information tends to alleviate rent dissipation. Our results have a natural interpretation in terms of eroding reputations. |
| JEL: | C73 D82 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:ide:wpaper:21999&r=gth |
| By: | Luca Di Corato (Swedish University of Agricultural Sciences) |
| Abstract: | A government bargains a mutually convenient agreement with a multinational corporation to extract a natural resource. The corporation bears the initial investment and earns as a return a share on the profits. The host country provides access and guarantee conditions of operation. Being the investment totally sunk, the corporation must account in its plan not only for uncertainty on market conditions but also for the threat of nationalization. In a real options framework where the government holds an American call option on nationalization we show under which conditions a Nash bargaining is feasible and leads to attain a cooperative agreement maximizing the joint venture surplus. We find that the threat of nationalization does not affect the investment time trigger but only the feasible bargaining set. Finally, we show that the optimal sharing rule results from the way the two parties may differently trade off rents with option value. |
| Keywords: | Real Options, Nash Bargaining, Expropriation, Natural Resources, Foreign Direct Investment |
| JEL: | C7 D8 K3 F2 O1 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2010.5&r=gth |