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on Game Theory |
| By: | Christophe Labreuche (Thales Research & Technology); Michel Grabisch (Centre d'Economie de la Sorbonne) |
| Abstract: | Bi-cooperative games have been introduced by Bilbao as a generalization of classical cooperative games, where each player can participate positively to the game (defender), negatively (defeater), or do not participate (abstentionist). In a voting situation (simple games), they coincide with ternary voting game of Felsenthal and Mochover, where each voter can vote in favor, against or abstain. In this paper, we propose a definition of value or solution concept for bi-cooperative games, close to the Shapley value, and we give an interpretation of this value in the framework of (ternary) simple games, in the spirit of Shapley-Shubik, using the notion of swing. Lastly, we compare our definition with the one of Felsenthal and Machover, based on the notion of ternary roll-call, and the Shapley value of multi-choice games proposed by Hsiao and Ragahavan. |
| Keywords: | Cooperative game theory, bi-cooperative games, power index, Shapley value. |
| JEL: | C71 |
| Date: | 2006–03 |
| URL: | http://d.repec.org/n?u=RePEc:mse:wpsorb:b06023&r=gth |
| By: | Luca Anderlini; Dino Gerardi; Roger Lagunoff (Department of Economics, Georgetown University) |
| Abstract: | We analyze “dynastic” repeated games. A stage game is repeatedly played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. When all players observe the past history of play, the standard repeated game and the dynastic game are equivalent In our model all players live one period and do not observe the history of play that takes place before their birth, but instead receive a private message from their immediate predecessors. Under very mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained as a Sequential Equilibrium of the dynastic repeated game with private communication. The result applies to any stage game for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize entirely when a Sequential Equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a Subgame Perfect Equilibrium of the standard repeated game. For this to be the case it must be that the players’ equilibrium beliefs violate a condition that we term “Inter-Generational Agreement.” Classification-JEL Codes: C72, C73, D82 |
| Keywords: | Dynastic Repeated Games, Private Communication, Folk Theorem |
| URL: | http://d.repec.org/n?u=RePEc:geo:guwopa:gueconwpa~06-06-01&r=gth |
| By: | M.R. Feix (SUBATECH/EMN); D. Lepelley (CERESUR); V. Merlin (CREM – CNRS); J.L. Rouet (MAPMO – CNRS) |
| Abstract: | Even, and in fact chiefly, if two or more players in a voting game have on a binary issue independent opinions, they may have interest to form a single voting alliance giving an average gain of influence for all of them. Here, assuming the usual independence of votes, we first study the alliance voting power and obtain new results in the so-called asymptotic limit for which the number of players is large enough and the alliance weight remains a small fraction of the total of the weights. Then, we propose to replace the voting game inside the alliance by a random game which allows new possibilities. The validity of the asymptotic limit and the possibility of new alliances are examined by considering the decision process in the Council of Ministers of the European Union. |
| URL: | http://d.repec.org/n?u=RePEc:tut:cremwp:200605&r=gth |
| By: | Pierre-André Chiappori (Department of Economics, University of Chicago); Olivier Donni (THEMA, Université de Cergy-Pontoise) |
| Abstract: | Consider a model of bargaining, in which two players, 1 and 2, share a pie of size $y$. The bargaining environment is described by a set of parameters $\lambda$ that may affect agents' preferences over the agreement sharing, the status quo outcome, or both. The outcomes (i.e., whether an agreement is reached, and if so the individual shares) and the environment (including the size of the pie) are known, but neither the agents' utilities nor their threat points. Assuming that the agents adopt a Nash bargaining solution, we investigate the empirical content of this assumption. We first show that in the most general framework, any outcome can be rationalized as a Nash solution. However, if (i) the size of the pie $y$ does not influence the players' threat points and (ii) there exist (at least) two parameters $\lambda_1$ and $\lambda_2$ that are player-specific, in the sense that $\lambda_i$ does not influence the utility or the threat point of player $j \neq i$, then Nash bargaining generates strong testable restrictions. Moreover, the underlying structure of the bargaining, i.e., the players? utility and threat point functions, can be recovered under slightly more demanding conditions. |
| Keywords: | Keywords: Bargaining Game, Nash Solution, Testability, Identifiability, Cardinal Utility |
| JEL: | C71 C72 |
| Date: | 2005–02 |
| URL: | http://d.repec.org/n?u=RePEc:ema:worpap:2006-07&r=gth |
| By: | Alberto Fogale; Paolo Pellizzari; Massimo Warglien (Department of Applied Mathematics, University of Venice) |
| Abstract: | We study a modified version of the coordination game presented in [van Huyck et al., 1994], where a representative selection dynamics was proposed to explain experimental data. Assuming that the agents adjust their moves in the direction of the best response, we derive a formal analysis of the stability of the equilibria. We show by simulation that the interior equilibrium is robustly reached even when considerable heterogeneity is allowed among the agents. Our truly multi-agent game is capable of approximating quite well both the ãmedianä game convergence and the experimental data. |
| Keywords: | Coordination game, Equilibrium selection, Best reply dynamics |
| JEL: | C71 D83 C63 C15 |
| Date: | 2006–05 |
| URL: | http://d.repec.org/n?u=RePEc:vnm:wpaper:135&r=gth |
| By: | Nageeb Ali; Navin Kartik |
| Date: | 2006–05–10 |
| URL: | http://d.repec.org/n?u=RePEc:cla:najeco:321307000000000016&r=gth |
| By: | Dechenaux, Emmanuel; Kovenock, Dan |
| Abstract: | This paper contributes to the study of tacit collusion by analyzing infinitely reaped multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under both the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that when each firm sets a price-quantity pair specifying the firm’s minimum acceptable price and the maximum quantity the firm is willing to sell at this price, there exists a range of discount factors for which the monopoly outcome with equal sharing is sustainable in the uniform price auction, but not in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this outcome. We extend these results to the case where firms may set bids that are arbitrary step functions of price-quantity pairs with any finite number of price steps. Surprisingly, under the Maximum Accepted Price rule, firms need employ no more than two price steps to minimize the value of the discount factor above which the perfectly collusive outcome with equal sharing is sustainable on a stationary path. Under the Market Clearing Price rule, only one step is required. That is, within the class of step bidding functions with a finite number of steps, maximal collusion is attained with simple price-quantity strategies exhibiting capacity withholding. |
| Keywords: | Auction ; Capacity ; Collusion ; Electricity Market ; Supply Function |
| JEL: | D43 D44 L13 L41 L94 |
| Date: | 2005–03 |
| URL: | http://d.repec.org/n?u=RePEc:pur:prukra:1174&r=gth |
| By: | Maarten C.W. Janssen (Erasmus Universiteit Rotterdam) |
| Abstract: | This paper argues that the notion of focal points is important in understanding bargaining processes. Recent literature confines a discussion of the usefulness of the notion to coordination problems and when bargaining experiments result in outcomes that are inconsistent with a straightforward interpretation of economic theory, some notion of ‘fairness’ is invoked. This paper uses symmetry requirements to formalize the notion of focal points. By doing so, it explains the focality of equal split division and it re-interprets recent experimental evidence in bargaining games. Experimental economists should try to empirically disentangle the importance of focal points from other explanatory factors (such as fairness). One way to do so, would be to study modal (instead of average) responses more systematically. Future theoretical research should focus on the strategic implications of proposing a frame (focal point) to conceive of the bargaining problem. |
| Keywords: | Bargaining; Game Perceptions; Focal Points |
| JEL: | C78 C91 |
| Date: | 2006–04–26 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20060040&r=gth |
| By: | Godefroy DangNguyen (ENST-B); Thierry Pénard (CREM-CNRS) |
| Abstract: | The aim of this paper is to understand the rationale of cooperation within online sharing communities. How can we explain the extent of cooperative interactions between anonymous distant Internet users ? We build a game theoretic framework to study the exchange of services within virtual community like in a peer-to-peer network. We show that the coexistence of contributors and free-riders is often a stable situation. We also examine the optimal incentive mechanisms to stimulate contributions by community members. |
| Keywords: | Online communities, Internet,free riding |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:tut:cremwp:200601&r=gth |
| By: | Sanjeev Goyal; Marcel Fafchamps; Marco J. van der Leij |
| Abstract: | This paper examines the existence and magnitude of network effects in the matching of workteams. We study the formation of co-author relations among economists over a thirty year period. Our principal finding is that a collaboration emerges faster among two authors if they are closer in the social network of economists. This proximity effect on collaboration is strong and robust but only affects initial collaboration. It has no positive influence on subsequent co-authorship. We also provide some evidence that matching depends on experience, junior authors being more likely to collaborate with senior authors. |
| Date: | 2006–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:esx:essedp:611&r=gth |