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on Game Theory |
| By: | Irene Valsecchi (University of Milano-Bicocca) |
| Abstract: | The paper shows that Perfect Bayesian equilibria need not be unique in the strategic communication game of Crawford and Sobel (1982). First, different equilibrium partitions of the state space can have equal cardinality, despite fixed prior beliefs. Hence, there can be different equilibrium action profiles with the same size. Second, provided a Perfect Bayesian equilibrium exists, different message rules and beliefs can hold in other equilibria inducing the same action profile. |
| Keywords: | Sender-Receiver Games, Strategic Information Transmission |
| JEL: | D83 |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2009.19&r=gth |
| By: | Kris De Jaegher; Stephanie Rosenkranz |
| Abstract: | In a two-player stag hunt with asymmetric information, players may lock each other into requiring a large number of confirmations and confirmations of confirmations from one another before eventually acting. This intuition has been formalized in the electronic mail game (EMG). The literature provides extensions on the EMG that eliminate inefficient equilibria, suggesting that no formal rules are needed to prevent players from playing inefficiently. The present paper investigates whether these results extend to the multi-player EMG. We show that standard equilibrium refinements cannot eliminate inefficient equilibria. While two players are predicted to play efficiently, many players need formal rules telling them when who talks to whom. |
| Keywords: | Multi-Player Electronic Mail Game, Collective Action, Communication Networks |
| JEL: | D82 D85 D71 |
| Date: | 2009–04 |
| URL: | http://d.repec.org/n?u=RePEc:use:tkiwps:0906&r=gth |
| By: | Jeanne Hagenbach (Centre d'Economie de la Sorbonne) |
| Abstract: | In the dynamic game we consider, players are the members of a fixed network. Everyone is initially endowed with an information item that he is the only paper to hold. Players are offered a finite number of periods to centralize the initially dispersed items in the hands of any one member of the network. In every period, each agent strategically chooses whether or not to transmit the items he holds to this neighbors in the network. The sooner all the items are gathered by any individual, the better it is for the group of players as a whole. Besides, the agent who first centralizes all the items is offered an additional reward that he keeps for himself. In this framework where information transmission is strategic and physically restricted, we provide a necessary and sufficient condition for a group to pool information items in every equilibrium. This condition is independent of the network structure. The architecture of links however affects the time needed before items are centralized in equilibrium. This paper provides theoretical support to Bonacich (1990)'s experimental results. |
| Keywords: | Social network, social dilemma, dynamic network game, strategic communication. |
| JEL: | D83 C72 L22 |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:09011&r=gth |
| By: | Kris De Jaegher |
| Abstract: | This paper considers a multi-player stag hunt where players are either available for action or not, and where players additionally differ in their degree of conservatism, i.e. in the threshold of players that need to act along with them before they see benefits in collective action. Minimal sufficient networks, which depending on their thresholds allow players to achieve just enough interactive knowledge about each other's availability to act, take the form of hierarchies of cliques (Chwe, RES, 2000). We show that any typical threshold game has a plethora of such networks, so that players seem to face a large degree of strategic uncertainty over which network to use. The plethora of networks includes cases where the structure of the network infects players into acting more conservatively than is reflected in their thresholds. An extreme case of this is the core-periphery network, where each player acts as conservatively as the most conservative player in the population. Because of this feature, the core-periphery network is minimal sufficient for all possible populations. Players can thus solve the strategic uncertainty arising from the multiplicity of minimal sufficient networks by using the all-purpose core-periphery network. |
| Keywords: | Threshold Game, Common Knowledge, Network Formation, Collective Action. |
| JEL: | D82 D85 D71 |
| Date: | 2009–04 |
| URL: | http://d.repec.org/n?u=RePEc:use:tkiwps:0907&r=gth |
| By: | Franck Delaplace (IBISC - Informatique, Biologie Intégrative et Systèmes Complexes - CNRS : FRE3190 - Université d'Evry-Val d'Essonne); Pierre Lescanne (LIP - Laboratoire de l'Informatique du Parallélisme - INRIA - CNRS : UMR5668 - Université Claude Bernard - Lyon I - Ecole Normale Supérieure de Lyon - ENS Lyon) |
| Abstract: | This paper proposes a new framework for cooperative games based on mathematical relations. Here cooperation is defined as a supportive partnerships represented by a directed network between players (aka hedonic relation). We examine in a specific context, modeled by abstract games how a change of supports induces a modification of strategic interactions between players. Two levels of description are considered: the first one describes the support network formation whereas the second one models the strategic interactions between players. Both are described in a unified formalism, namely CP~game. Stability conditions are stated, emphasizing the connection between these two levels. We also stress the interaction between updates of supports and their impact on the evolution of the context. |
| Keywords: | Cooperative Game, Network, Stability, Hedonic Relation |
| Date: | 2009–05–15 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00382514_v2&r=gth |
| By: | Matteo M. Galizzi |
| Abstract: | In the context of international gas markets, we investigate the interaction between price formation and communication networks in a bilateral duopoly with heterogeneous buyers. Given a particular buyers-sellers network graph, prices are formed as the outcome of dynamic decentralized negotiations among traders. We characterize, for any network structure, the full set of sub-game perfect Nash equilibria in pure and stationary strategies (PSSPNE) of the non-cooperative bargaining game with random order of proposals and simultaneous responses. Depending on the inter-temporal discount factor and the dispersion of reservation values across buyers, negotiations may lead, even in a completely connected buyers-sellers network, to multiple equilibria, co-existence of different prices, delays in trade and inefficient allocations. The endogenous bargaining power of each trader as a function of her position in the communication network is derived by comparing traders' payoffs across networks. |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:ubs:wpaper:0906&r=gth |
| By: | Jeanne Hagenbach (Centre d'Economie de la Sorbonne); Frédéric Koessler (Paris-Jourdan Sciences Economiques (PSE)) |
| Abstract: | We consider situations in which individuals would like to choose an action which is close to that of others, as well as close to a state of nature, with the ideal proximity to the state varying across agents. Before this coordination game is played, a cheap-talk communication stage is offered to the indivisuals who decide to whom they reveal their private information about the state. The information transmission occurring in the communication stage is characterized by a strategic communication network. We provide an explicit link between players' preferences and the equilibrium strategic communication networks. A key feature of our equilibrium characterization is that whether communication takes place between two agents not only depends on the conflict of interest between these agents, but also on the number and preferences of the other agents with whom they communicate. Apart from some specific cases, the equilibrium communication networks are quite complex despite our simple one-dimensional description of preference heterogeneity. In general, strategic communication networks cannot be completely Pareto-ranked, but expected social welfare always increases as the communication network expands. |
| Keywords: | Cheap talk, coordination, incomplete information, networks. |
| JEL: | C72 D82 D83 D85 |
| Date: | 2009–02 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:09005&r=gth |
| By: | Hsiao, Chih-Ru; Chiou, Wen-Lin |
| Abstract: | The H&R multi-choice Shapley value defined by Hsiao and Raghavan for multi-choice cooperative game is redundant free. If the H&R value is used as the solution of a game, there won't be any objection to a player's taking redundant actions. Therefore, the spirit of the law on equal job opportunities is automatically fulfilled. |
| Keywords: | Shapley value; multi-choice cooperative game; redundant free |
| JEL: | C7 K31 |
| Date: | 2009–05–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:15285&r=gth |
| By: | Angelo Antoci; Paolo Russu; Luca Zarri |
| Abstract: | An oft-cited and robust result from Public Goods Game experiments is that, when subjects start playing, the aggregate level of contributions is significantly different from zero. At the same time, a sizeable proportion of players free ride from the outset. Behavioural economics has persuasively shown that these laboratory findings are compatible with the presence of motivationally heterogeneous agents, displaying both standard, self-centred preferences and non-standard, interdependent preferences. However, at the theoretical level, economists would prefer to account for motivational heterogeneity endogenously, instead of simply assuming it from the outset. Our work provides such endogenisation, by assuming that social evolution is driven by material payoffs only. By separately focusing on different types of ‘experimentally salient’ pro-social players (such as Reciprocators, Strong Reciprocators and Altruists), we are able to shed light – to our knowledge, for the first time, within the public good framework – on the evolutionary stability of two-type populations consisting of positive proportions of both ‘nice’ and ‘mean’ guys. |
| Keywords: | Free Riding; Strong Reciprocity; Altruism; Nonstrategic Punishment; Public Goods Game; Evolutionary Game Theory. |
| JEL: | C7 D6 H8 Z1 |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:ver:wpaper:55&r=gth |
| By: | Edi Karni |
| Abstract: | This paper presents a complete, choice-based, axiomatic Bayesian decision theory. It introduces a new choice set consisting of information-contingent plans for choosing actions and bets and subjective expected utility model with effect-dependent utility functions and action-dependent subjective probabilities which, in conjunction with the updating of the probabilities using Bayes' rule, gives rise to a unique prior and a set of action-dependent posterior probabilities representing the decision maker's prior and posterior beliefs. |
| Date: | 2009–05 |
| URL: | http://d.repec.org/n?u=RePEc:jhu:papers:550&r=gth |
| By: | Berg Anita H.J. van den; Herings P. Jean-Jacques; Peters Hans J.M. (METEOR) |
| Abstract: | We analyze strategic firm behavior in settings where the production stage is followed by several periods during which only sales take place. We analyze the dynamics of the market structure, the development of prices and sales over time, and the implications for profits and consumer surplus. Two specific settings are analyzed. In the first, a firm can commit up-front to a sales strategy that does not depend on the actual sales of its competitor. In this case there is a unique Nash equilibrium and price increases over time. In the second setting,there is no commitment and firms can adjust their sales in response to observed supply of their competitor in the previous period. It is shown that in this case a subgame perfect Nash equilibrium does not always exist. Equilibria can have surprising features. For some parameter constellations, price may decrease over time. It is also possible that the firm increases its pro t by destroying some of its production. When firms have equal size, the equilibrium outcome is the same in both the commitment and the non-commitment setting. In general, the setting without commitment is bene cial to the larger firm, whereas the setting with commitment leads to higher pro ts for the smaller firm. |
| Keywords: | mathematical economics; |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2009020&r=gth |
| By: | Roland Kirstein (Faculty of Economics and Management, Otto-von-Guericke University Magdeburg) |
| Abstract: | After Porsche SE took over Volkswagen AG, its supervisory board consists of three groups: The Porsche shareholders hold 6 seats, while the 324,000 Volkswagen employees and the 12,000 Porsche employees will be represented by 3 delegates each. This paper perceives each of these three groups as unitary players and presents a power-index analysis of this supervisory board. It shows that, unless the Porsche employees are made completely powerless, Porsche and VW employees will have identical power regardless of the actual distribution of seats on the employees' side. This analysis demonstrates that the request of the Volkswagen employees (for more seats than the Porsche employees in the future supervisory board) is unfounded. |
| Keywords: | Banzhaf power-index, supervisory board, societas europeae |
| JEL: | C71 D72 K22 M21 |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:mag:wpaper:09007&r=gth |