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on Game Theory |
| By: | James W. Bono; David H. Wolpert |
| Abstract: | Conventionally, game theory predicts that the mixed strategy profile of players in a noncooperative game will satisfy some equilibrium concept. Relative probabil- ities of the strategy profiles satisfying the concept are unspecified, and all strategies not satisfying it are implicitly assigned probability zero. As an alternative, we re- cast the prediction problem of game theory as statistically estimating the strategy profile, from "data" that consists of the game specification. This replaces the focus of game theory, on specifying a set of "equilibrium" mixed strategies, with a new focus, on specifying a probability density over all mixed strategies. We explore a Bayesian version of such a Predictive Game Theory (PGT). We show that for some games the peaks of the posterior over strategy profiles approximate quantal response equilibria. We also show how PGT provides a best single prediction for any noncooperative game, i.e., a universal refinement. We also show how regula- tors can use PGT to make optimal decisions in situations where conventional game theory cannot provide advice. |
| Keywords: | Quantal Response Equilibrium, Bayesian Statistics, Entropic prior, Maximum entropy |
| JEL: | C02 C11 C70 C72 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:amu:wpaper:2009-20&r=gth |
| By: | James W. Bono; David H. Wolpert |
| Abstract: | It is known that a player in a noncooperative game can benefit by publicly re- stricting their possible moves before start of play. We show that, more generally, a player may benefit by publicly committing to pay an external party an amount that is contingent on the game's outcome. We explore what happens when external parties (who we call game miners) discover this fact and seek to profit from it by entering an outcome-contingent contract with the players. We analyze various bargaining games between miners and players for determining such an outcome- contingent contract. We establish restrictions on the strategic settings in which a game miner can profit, and bounds on the game miner's profit given various structured bargaining games. These bargaining games include playing the players against one another, as well as allowing the players to pay the miner(s) for exclu- sivity and first-mover advantage. We also establish that when all players can enter contracts with miners, to guarantee the existence of equilibria it is necessary to assume that players can randomize over the contracts they make. |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:amu:wpaper:2009-10&r=gth |
| By: | Ralph-C Bayer (School of Economics, University of Adelaide); Elke Renner (School of Economics, University of Nottingham); Rupert Sausgruber (Department of Economics, University of Copenhagen) |
| Abstract: | We use a limited information environment to mimic the state of confusion in an experimental, repeated public goods game. The results show that reinforcement learning leads to dynamics similar to those observed in standard public goods games. However, closer inspection shows that individual decay of contributions in standard public goods games cannot be fully explained by reinforcement learning. According to our estimates, learning only accounts for 41 percent of the decay in contributions in standard public goods games. The contribution dynamics of subjects, who are identi?ed as conditional cooperators, di®er strongly from the learning dynamics, while a learning model estimated from the limited information treatment tracks behavior for subjects, who cannot be classi?ed as conditional cooperators, reasonably well. |
| Keywords: | public goods experiments, learning, limited information, confusion, conditional cooperation |
| JEL: | C90 D83 H41 |
| Date: | 2009–10 |
| URL: | http://d.repec.org/n?u=RePEc:cdx:dpaper:2009-18&r=gth |
| By: | James W. Bono; David H. Wolpert |
| Abstract: | We extend a recently introduced approach to the positive problem of game theory, Predictive Game Theory (PGT Wolpert (2008). In PGT, modeling a game results in a probability distribution over possible behavior profiles. This contrasts with the conventional approach where modeling a game results in an equilibrium set of possible behavior profiles. We analyze three PGT models. Two of these are based on the well-known quantal response and epsilon equilibrium concepts, while the third is entirely new to the economics literature. We use a Cournot game to demonstrate how to use our extension of PGT, concentrating on model combination, modeler uncertainty, and mechanism design. In particular, we emphasize how PGT allows a modeler to perform prediction and mechanism design in a manner that is fully consistent with decision theory. We do this even in situations where conventional approaches yield multiple equilibria, an ability that is necessary for a fully decision theoretic mechanism design. Where possible, PGT results are compared against equilibrium set analogs. |
| Date: | 2009–08 |
| URL: | http://d.repec.org/n?u=RePEc:amu:wpaper:2009-11&r=gth |
| By: | Elie Appelbaum (York University, Toronto) |
| Abstract: | This paper shows that the Rubinstein alternating offers model can be modified to provide a Pareto superior outcome in the context of the right-to-manage union-firm bargaining. Two examples of bargaining protocols that yield a superior outcome are provided. In the first example, the union and the firm engage in a game in which the order of play is determined as part of the bargaining. We show that the game has a unique subgame perfect equilibrium in which the firm always moves first in the wage bargaining game and the equilibrium wage is, therefore, unique. In the second example we examine a two-part-tariff alternating offers bargaining protocol, where the firm and the union bargain over the wage and transfer payments. We show that this bargaining protocol has a Pareto efficient, unique subgame perfect equilibrium. Thus, although the parties do not bargain over the level of employment, the outcome under this protocol is, nevertheless, “socially” optimal. |
| Keywords: | Union Wage premium, Efficient Bargaining, Right to Manage |
| JEL: | J51 J52 J53 C70 |
| Date: | 2009–02 |
| URL: | http://d.repec.org/n?u=RePEc:yca:wpaper:2009_02&r=gth |
| By: | Nicholas E. Burger; Charles D. Kolstad |
| Abstract: | The literature on voluntary provision of public goods includes recent theoretical work on the formation of voluntary coalitions to provide public goods. Theory is ambiguous on the equilibrium coalition size and contribution rates. We examine the emergence of coalitions, their size, and how uncertainty in public goods provision affects contribution levels and coalition size. We find that contributions decrease when public good returns are uncertain but increase when individuals can form a coalition to provide the good. Contrary a core theoretical result, we find that coalition size increases when the public good benefits are higher. Uncertainty has no effect on coalition size. |
| JEL: | C7 C91 C92 H23 H4 H41 Q5 Q54 |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:15543&r=gth |
| By: | Jacob K. Goeree; Yuanchuan Lien |
| Abstract: | When goods are substitutes, the Vickrey auction produces efficient, core outcomes that yield competitive seller revenues. In contrast, with complements, the Vickrey outcome, while efficient, is not necessarily in the core and revenue can be very low. Non-core outcomes may be perceived as unfair since there are bidders willing to pay more than the winners' payments. Moreover, non-core outcomes render the auction vulnerable to defections as the seller can attract better offers afterwards. To avoid instabilities of this type, Day and Raghavan (2007) and Day and Milgrom (2007) have suggested to adapt the Vickrey pricing rule. For a simple environment with private information, we show that the resulting auction format yields lower than Vickrey revenues and inefficient outcomes that are on average further from the core than Vickrey outcomes. More generally, we prove that the Vickrey auction is the unique core-selecting auction. Hence, when the Vickrey outcome is not in the core, no Bayesian incentive-compatible core-selecting auction exists. Our results further imply that the competitive equilibrium cannot be implemented when goods are not substitutes. Moreover, even with substitutes, the competitive equilibrium can only be implemented when it coincides with the Vickrey outcome. |
| Keywords: | Core outcomes, Vickrey auction, substitutes, complements, competitive equilibrium, Bayesian implementability |
| JEL: | D44 |
| Date: | 2009–11 |
| URL: | http://d.repec.org/n?u=RePEc:zur:iewwpx:452&r=gth |