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on Game Theory |
| By: | Carmelo Rodriguez-Alvarez |
| Abstract: | We analyze coalition formation problems in which a group of agents is partitioned into coalitions and agents' preferences only depend on the coalition they belong to. We study rules that associate to each profile of agents' preferences a partition of the society. We focus on strategyproof rules on restricted domains of preferences, as the domains of additively representable or separable preferences. In such domains, only single-lapping rules satisfy strategy-proofness, individual rationality, non-bossiness, and flexibility. Single-lapping rules are characterized by severe restrictions on the set of feasible coalitions. These restrictions are consistent with hierarchical organizations and imply that single-lapping rules always select core-stable partitions. Thus, our results highlight the relation between the non-cooperative concept of strategy-proofness and the cooperative concept of core-stability. We analyze the implications of our results for matching problems |
| Date: | 2005–09 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:we055525&r=gth |
| By: | Giovanna Devetag; Massimo Warglien |
| Abstract: | It has been suggested that players often produce simplified and/or misspecified mental representations of interactive decision problems (Kreps, 1990). We submit that the relational structure of players’ preferences in a game induces cognitive complexity, and may be an important driver of such simplifications. We provide a formal classification of order structures in two-person normal form games based on the two properties of monotonicity and projectivity, and present experiments in which subjects must first construct a representation of games of different relational complexity, and subsequently play the games according to their own representation. Experimental results support the hypothesis that relational complexity matters. More complex games are harder to represent, and this difficulty is correlated with measures of short term memory capacity. Furthermore, most erroneous representations are less complex than the correct ones. In addition, subjects who misrepresent the games behave consistently with such representations according to simple but rational decision criteria. This suggests that in many strategic settings individuals may act optimally on the ground of simplified and mistaken premises. |
| Keywords: | pure motive, mixed motive, preferences, bi-orders, language, cognition, projectivity, monotonicity, short term memory, experiments |
| JEL: | C70 C72 C91 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:trn:utwpce:0504&r=gth |
| By: | David A. Miller (UCSD) |
| Abstract: | In a repeated game with private information, a perfect public equilibrium (PPE) can break down if communication is not necessarily simultaneous or if players can “spy” on each others’ information. An ex post perfect public equilibrium (EPPPE) is a PPE that is ex post incentive compatible in each stage game; unlike PPE, EPPPE is robust under to any communication protocol, and to spying. However, robustness comes at a cost to the players: in many games, efficient payoffs in the corresponding static mechanism design problem cannot be supported as average payoffs in an EPPPE, even when players are patient. In two- player repeated allocation games, an optimal EPPPE never employs a (static) efficient outcome function in any stage game. Instead, the players always prefer to give up some static efficiency by sometimes allocating to the player with the lower valuation. Under independent valuations, optimal equilibria are often stationary, but when valuations are globally interdependent, optimal equilibria are never stationary. Applied to the problem of collusion with hidden costs, these results yield new insights into the phenomenon of price wars in collusive equilibria. |
| Keywords: | repeated games, private information, ex post incentive compatibility, price wars |
| JEL: | C72 C73 D82 L13 |
| Date: | 2005–10–06 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpga:0510002&r=gth |
| By: | John Duffy (University of Pittsburgh); M. Utku Unver (University of Pittsburgh) |
| Abstract: | Many internet auction sites implement ascending-bid, second-price auctions. Empirically, lastminute or “late” bidding is frequently observed in “hard-close” but not in “soft-close” versions of these auctions. In this paper, we introduce an independent private-value repeated internet auction model to explain this observed difference in bidding behavior. We use finite automata to model the repeated auction strategies. We report results from simulations involving populations of artificial bidders who update their strategies via a genetic algorithm. We show that our model can deliver late or early bidding behavior, depending on the auction closing rule in accordance with the empirical evidence. As an interesting result, we observe that hard-close auctions raise less revenue than softclose auctions. We also investigate interesting properties of the evolving strategies and arrive at some conclusions regarding both auction designs from a market design point of view. |
| JEL: | C8 |
| Date: | 2005–10–01 |
| URL: | http://d.repec.org/n?u=RePEc:wpa:wuwpco:0510001&r=gth |
| By: | Patrick Bajari; Jeremy T. Fox |
| Abstract: | We empirically study bidding in the C Block of the US mobile phone spectrum auctions. Spectrum auctions are conducted using a simultaneous ascending auction design that allows bidders to assemble packages of licenses with geographic complementarities. While this auction design allows the market to find complementarities, the auction might also result in an inefficient equilibrium. In addition, these auctions have equilibria where implicit collusion is sustained through threats of bidding wars. We estimate a structural model in order to test for the presence of complementarities and implicit collusion. The estimation strategy is valid under a wide variety of alternative assumptions about equilibrium in these auctions and is robust to potentially important forms of unobserved heterogeneity. We make suggestions about the design of future spectrum auctions. |
| JEL: | L0 L5 C1 |
| Date: | 2005–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:11671&r=gth |