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on Game Theory |
| By: | Lijue Xie (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | Bicooperative games generalize classical cooperative games in the sense that a player is allowed to play in favor or against some aim, besides non participation. Bicapacities are monotonic bicooperative games, they are useful in decision making where underlying scales are of bipolar nature, i.e., they distinguish between good/satisfactory values and bad/unsatisfactory ones. We propose here a more general framework to represent such situations, called bipolar game. We study the problem of finding the core of such games, i.e., the<br />set of additive dominating games. |
| Keywords: | fuzzy measure, bicapacity, cooperative game, bipolar scale,<br />core |
| Date: | 2007–05 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00187162_v1&r=gth |
| By: | Carmona, Guilherme |
| Abstract: | We consider games with a continuum of players and intermediate prefer- ences. We show that any such game has a Nash equilibrium that induces a partition of the set of attributes into a bounded number of convex sets with the following property: all players with an attribute in the interior of the same element of the partition play the same action. Furthermore, if the game induces an absolutely continuous distribution (with respect to the Lebesgue measure) on the attribute space, then we can strengthen the conclusion by showing that all players with an attribute in the same element of the partition play the same action. |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:unl:unlfep:wp523&r=gth |
| By: | Philippe Bich (Centre d'Economie de la Sorbonne) |
| Abstract: | Answering to an open question of Herings et al. (see [3]), one extends their fixed point theorem to mappings defined on convex compact subset of Rn, and not only polytopes. Such extension is important in non-cooperative game theory, where typical strategy sets are convex and compact. An application in game theory is given. |
| Keywords: | Discontinuous game, Nash equilibrium, fixed point theorem. |
| JEL: | C60 |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:b07069&r=gth |
| By: | Marc Oliver Rieger (University of Zurich) |
| Abstract: | We study how the framework of classical game theory changes when the preferences of the players are described by Prospect Theory instead of Expected Utility Theory. Specifically, we study the influence of framing effect and probability weighting on the existence and specific structure of Nash equilibria in pure and mixed strategies for finite games. We demonstrate that in games representing typical interactions in societies, probability weighting of the players can lead to larger common wealth and is, under weak assumptions,evolutionary stable. This observation may provide a possible explanation for the validity of Prospect Theory as a descriptive model in human behavior. |
| Keywords: | Prospect Theory, Existence of Nash Equilibria, Evolutionary stability. |
| JEL: | C70 C73 D81 |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp0729&r=gth |
| By: | Alexander Elbittar; Rodrigo Harrison; Roberto Muñoz |
| Date: | 2007–11–19 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:122247000000001708&r=gth |
| By: | Dziubinski, Marcin; Roy, Jaideep |
| Abstract: | The paper studies an evolutionary model where players from a given population are randomly matched in pairs each period to play a co- ordination game. At each instant, a player can choose to adopt one of the two possible behavior rules, called the rational rule and the as- piring rule, and then take actions prescribed by the chosen rule. The choice between the two rules depends upon their relative performance in the immediate past. We show that there are two stable long run outcomes where either the rational rule becomes extinct and all play- ers in the population achieve full eciency, or that both the behavior rules co-exist and there is only a partial use of ecient strategies in the population. These ndings support the use of the aspiration driven behavior in several existing studies and also help us take a comparative evolutionary look at the two rules in retrospect. |
| Keywords: | Co-evolution; Aspirations; Best-response; Random matching; Coordination games |
| JEL: | C73 C72 |
| Date: | 2007–11–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:5941&r=gth |
| By: | Mark W. Nichols (Department of Economics, University of Nevada, Reno); Michael J. Radzicki (Department of Social Science and Policy Studies, Worcester Polytechnic Institute) |
| Abstract: | Recently, computer simulation, particularly agent-based modeling, has grown in popularity as a method to uncover macro patterns and developments that emerge from simple micro behavior. The present paper combines both techniques by using protocol analysis to uncover player strategies in an experiment and encoding those strategies in an agent-based computer simulation. In particular, Keynes’ (1936) beauty contest analogy is simulated in a number-guessing context. Several researchers have conducted experiments asking subjects to play “p-beauty contest games” in order to compare the experimental results with those predicted by the game-theoretic, deductive reasoning concept of iterated dominance. Our results are compared with those found experimentally in order to demonstrate the usefulness of a combining agent-based modeling with protocol analysis. |
| Keywords: | Agent-Based modeling; Beauty contest games |
| JEL: | C15 E12 |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:unr:wpaper:07-010&r=gth |
| By: | Michel Benaim; Olivier Raimond |
| Date: | 2007–11–19 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000001702&r=gth |
| By: | Marco Pagnozzi (University of Napoli "Federico II" and CSEF) |
| Abstract: | Allowing resale in multi-object auctions increases bidders. incentives to jointly reduce demand, because resale increases low-value bidders’ willingness to pay and reduces high-value bidders’ willingness to pay. Therefore (unlike in single-object auctions), resale may reduce the seller’s revenue in multi-object auctions. However, we show that, under reasonable conditions, allowing resale and bundling the objects on sale are “complement strategies” for the seller – by bundling and allowing resale the seller earns a higher revenue than by selling the objects separately and/or not allowing resale. We also analyze how resale affects a bidder’s incentive to unilaterally reduce demand, and we show why allowing resale may reduce efficiency. |
| Keywords: | multi-object auctions, resale, bundling, demand reduction |
| JEL: | D44 |
| Date: | 2007–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:186&r=gth |
| By: | Carraro, Carlo; Sgobbi, Alessandra |
| Abstract: | The objective of this paper is to investigate the usefulness of non-cooperative bargaining theory for the analysis of negotiations on water allocation and management. We explore the impacts of different economic incentives, a stochastic environment and varying individual preferences on players’ strategies and equilibrium outcomes through numerical simulations of a multilateral, multiple issues, non-cooperative bargaining model of water allocation in the Piave River Basin, in the North East of Italy. Players negotiate in an alternating-offer manner over the sharing of water resources (quantity and quality). Exogenous uncertainty over the size of the negotiated amount of water is introduced to capture the fact that water availability is not known with certainty to negotiating players. We construct the players’ objective function with their direct input. We then test the applicability of our multiple players, multi-issues, stochastic framework to a specific water allocation problem and conduct comparative static analyses to assess sources of bargaining power. Finally, we explore the implications of different attitudes and beliefs over water availability. |
| Keywords: | bargaining; non-cooperative game theory; simulation models; uncertainty |
| JEL: | C61 C71 C78 |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:6585&r=gth |
| By: | Marc Oliver Rieger (ETH Zurich, Department of Mathematics); Mei Wang (University of Zurich, ISB) |
| Abstract: | We extend the original form of Prospect Theory by Kahneman and Tversky from finite lotteries to arbitrary probability distributions, thus paving the way for applications in economics and finance. Moreover, we suggest a method how to incorporate a crucial step of the “editing phase” into Prospect Theory and to remove in this way the discontinuity of the original model. |
| Keywords: | Prospect Theory, Cumulative Prospect Theory, continuity, probability weighting, first-order stochastic dominance. |
| JEL: | D81 |
| Date: | 2007–03 |
| URL: | http://d.repec.org/n?u=RePEc:chf:rpseri:rp0730&r=gth |