|
on Game Theory |
| By: | René van den Brink (Vrije Universiteit Amsterdam); Gerard van der Laan (Vrije Universiteit Amsterdam); Valeri Vasil'ev (Sobolev Institute of Mathematics, Novosibirsk) |
| Abstract: | A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff vectors to every TU-game. Some solutions that are based on distributing dividends are the Shapley value (being the single-valued solution distributing the dividends equally among the players in the corresponding coalitions) and the Selectope or Harsanyi set (being the set-valued solution that contains all possible distributions of the dividends among the players in the corresponding coalitions). In this paper we assume the players to be hierarchically ordered. We modify the concept of Harsanyi set to this context by taking into account this hierarchical order when distributing the dividends of the game. We show that the resulting new solution concept for games with ordered players, called the Restricted Harsanyi set, is fully characterized by a collection of seven logically independent properties. We also discuss an alternative modification of the Harsanyi set and a solution concept resulting from adapting the concept of Selectope to games with ordered players. Some applications show the usefulness of the Restricted Harsanyi set. |
| Keywords: | TU-game; Harsanyi dividends; Shapley value; Harsanyi set; Selectope; digraph |
| JEL: | C71 |
| Date: | 2007–01–02 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20060114&r=gth |
| By: | Jackson, Matthew O.; Yariv, Leeat |
| Date: | 2006–10 |
| URL: | http://d.repec.org/n?u=RePEc:clt:sswopa:1264&r=gth |
| By: | Santiago Sanchez-Pages; Marc Vorsatz |
| Abstract: | We analyze experimentally two sender-receiver games with conflictive preferences. In the first game, the sender can choose to tell the truth, to lie, or to remain silent. The latter strategy is costly and similar to an outside option. If sent, the receiver can either trust or distrust the sender’s message. In the second game, the receiver must decide additionally whether or not to costly punish the sender after having observed the history of the game. We investigate the existence of two kinds of social preferences: Lie-aversion and preference for truth-telling. In the first game, senders tell the truth more often than predicted by the sequential equilibrium concept, they remain silent frequently, and there exists a positive correlation between the probability of being truthful and the probability of remaining silent. Our main experimental result for the extended game shows that those subjects who punish the sender with a high probability after being deceived are precisely those who send fewer but more truthful messages. We then explore two formal models of the baseline game that can account for our experimental results. First, we fit the data to the logit agent quantal response equilibrium; secondly, we solve for the Perfect Bayesian Nash equilibria of a stylized version of the baseline game with two types of senders. The equilibrium predictions obtained in both cases are consistent with both preferences for truth-telling and lie-aversion although the latter seems to be more pronounced. |
| Keywords: | Experiment, Lie-Aversion, Social Preferences, Strategic Information Transmission, Truth-Telling. |
| JEL: | C72 C73 D83 |
| URL: | http://d.repec.org/n?u=RePEc:edn:esedps:155&r=gth |
| By: | Pedro Rey-Biel |
| Abstract: | We report experimental results on one-shot two person 3x3 constant sum games played by non-economists without previous experience in the laboratory. Although strategically our games are very similar to previous experiments in which game theory predictions fail dramatically, 80% of actions taken in our ex- periment coincided with the prediction of the unique Nash equilibrium in pure strategies and 73% of actions were best responses to elicited beliefs. We argue how social preferences, presentation effects and belief elicitation procedures may influence how subjects play in simple but non trivial games and explain the diferences we observe with respect to previous work. |
| Keywords: | Experiments, Constant Sum Games, Stated Beliefs |
| JEL: | C72 C91 D81 |
| Date: | 2007–01–15 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:676.07&r=gth |
| By: | Jean-Marc Bonnisseau; Vincent Iehlé |
| Abstract: | We prove the non-emptiness of the core of an NTU game satisfying a condition of payoff-dependent balancedness, based on transfer rate mappings. We also define a new equilibrium condition on transfer rates and we prove the existence of core payoff vectors satisfying this condition. The additional requirement of transfer rate equilibrium refines the core concept and allows the selection of specific core payoff vectors. Lastly, the class of parametrized cooperative games is introduced. This new setting and its associated equilibrium-core solution extend the usual cooperative game framework and core solution to situations depending on an exogenous environment. A non-emptiness result for the equilibrium-core is also provided in the context of a parametrized cooperative game. Our proofs borrow mathematical tools and geometric constructions from general equilibrium theory with non convexities. Applications to extant results taken from game theory and economic theory are given. |
| Keywords: | balancedness, cooperative game, core, parametrized game |
| JEL: | C60 C62 C71 D50 D51 |
| Date: | 2007–01–22 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:678.07&r=gth |
| By: | Luca Zarri (Corresponding author, Dipartimento di Scienze economiche (Università di Verona)) |
| Keywords: | Non-cooperative Games, Happiness, Morality. |
| JEL: | B41 C72 C91 D64 |
| Date: | 2006–12 |
| URL: | http://d.repec.org/n?u=RePEc:ver:wpaper:37&r=gth |
| By: | Gallice, Andrea |
| Abstract: | We introduce a simple procedure to be used for selecting the strategies most likely to be played by inexperienced agents who interact in one shot 2x2 games. We start with an axiomatic description of a function that may capture players' beliefs. Various proposals connected with the concept of mixed strategy Nash equilibrium do not match this description. On the other hand minimax regret obeys all the axioms. Therefore we use minimax regret to approximate players' beliefs and we let players best respond to these conjectured beliefs. When compared with existing experimental evidences about one shot matching pennies games, this procedure correctly indicates the choices of the vast majority of the players. Applications to other classes of games are also explored. |
| Keywords: | prediction; beliefs; mixed strategy Nash equilibrium; minimax regret; matching pennies; experiments. |
| JEL: | C72 C91 |
| Date: | 2007–01 |
| URL: | http://d.repec.org/n?u=RePEc:lmu:muenec:1365&r=gth |
| By: | Juan D. Carrillo; Thomas R. Palfrey |
| Date: | 2007–01–12 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:321307000000000754&r=gth |
| By: | Sudipta Sarangi; Pascal Billand; Christophe Bravard |
| Abstract: | This paper addresses the existence of Nash networks for the one-way flow model of Bala and Goyal (2000) in a number of different settings. First, we provide conditions for he existence of Nash networks in models where costs and values of links are heterogenous and players obtain resources from others only through the directed path between them. We find that costs of establishing links play a vital role in the existence of Nash networks. Next we examine the existence of Nash networks when there are congestion effects in the model. Then, we provide conditions for the existence of Nash networks in a model where a player’s payoff depends on the number of links she has established as well as on the number of links that other players in the population have created. More precisely, we show that convexity and increasing (decreasing) differences allow for the existence of Nash networks. |
| URL: | http://d.repec.org/n?u=RePEc:lsu:lsuwpp:2007-02&r=gth |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Stephen Morris (Dept. Economics, Princeton University) |
| Abstract: | We consider an single object auction environment with interdependent valuations and a generalized Vickrey-Clark-Groves allocation mechanism that allocates the object almost efficiently in a strict ex post equilibrium. If there is a significant amount of interdependence, there are multiple rationalizable outcomes of this direct mechanism and any other mechanism that allocates the object almost efficiently. This is true whatever the agents know about each others' payoff types or not. We consider an ascending price dynamic version of the generalized VCG mechanism. When there is complete information among the agents of their payoff types, we show that the almost efficient allocation is the unique backward induction (i.e., extensive form rationalizable) outcome of the auction, even when there are multiple rationalizable outcomes in the static version. This example illustrates the role that open auctions may play in obtaining efficient allocations by reducing strategic uncertainty. |
| Keywords: | Dynamic auction, Rationalizability, Extensive form, Uniqueness, Strategic uncertainty |
| JEL: | C79 D82 |
| Date: | 2007–01 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1600&r=gth |
| By: | Hoppe, Heidrun C.; Moldovanu, Benny; Ozdenoren, Emre |
| Abstract: | We study two-sided markets with heterogeneous, privately informed agents who gain from being matched with better partners from the other side. Agents are matched through an intermediary. Our main results quantify the relative attractiveness of a coarse matching scheme consisting of two classes of agents on each side, in terms of matching surplus (output), the intermediary's revenue, and the agents' welfare (defined by the total surplus minus payments to the intermediary). In a nutshell, our philosophy is that, if the worst-case scenario under coarse matching is not too bad relative to what is achievable by more complex, finer schemes, a coarse matching scheme will turn out to be preferable once the various transaction costs associated with fine schemes are taken into account. Similarly, coarse matching schemes can be significantly better than completely random matching, requiring only a minimal amount of information. |
| Keywords: | Matching; Nonlinear Pricing |
| JEL: | C78 D42 D82 L15 |
| Date: | 2007–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:6041&r=gth |