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on Game Theory |
| By: | Frank H. Page, Jr. (Department of Finance, University of Alabama); Myrna H. Wooders (Department of Economics, Vanderbilt University) |
| Abstract: | Given the preferences of players and the rules governing network formation, what networks are likely to emerge and persist? And how do individuals and coalitions evaluate possible consequences of their actions in forming networks? To address these questions we introduce a model of network formation whose primitives consist of a feasible set of networks, player preferences, the rules of network formation, and a dominance relation on feasible networks. The rules of network formation may range from noncooperative, where players may only act unilaterally, to cooperative, where coalitions of players may act in concert. The dominance relation over feasible networks incorporates not only player preferences and the rules of network formation but also assumptions concerning the degree of farsightedness of players. A specification of the primitives induces an abstract game consisting of (i) a feasible set of networks, and (ii) a path dominance relation defined on the feasible set of networks. Using this induced game we characterize sets of network outcomes that are likely to emerge and persist. Finally, we apply our approach and results to characterization of equilibrium of well known models and their rules of network formation, such as those of Jackson and Wolinsky (1996) and Jackson and van den Nouweland (2005). |
| Keywords: | Basins of attraction, network formation games, stable sets, path dominance core, Nash networks |
| JEL: | C71 C72 |
| Date: | 2006–06 |
| URL: | http://d.repec.org/n?u=RePEc:van:wpaper:0614&r=gth |
| By: | Vincent P. Crawford; Nagore Iriberri |
| Date: | 2006–07–31 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:321307000000000256&r=gth |
| By: | Julio J. Rotemberg |
| Abstract: | I suppose that people react with anger when others show themselves not to be minimally altruistic. With heterogeneous agents, this can account for the experimental results of ultimatum and dictator games. Moreover, it can account for the surprisingly large fraction of individuals who offer an even split, with parameter values that are more plausible than those required to explain outcomes in these experiments with the models of Levine (1998), Fehr and Schmidt (1999), Dickinson (2000), and Bolton and Ockenfels (2000). |
| Keywords: | Game theory |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedbwp:06-12&r=gth |
| By: | Joana Pais |
| Abstract: | Decentralized markets are modeled by means of a sequential game where, starting from any matching situation, firms are randomly given the opportunity to make job offers. In this random context, we prove the existence of ordinal subgame perfect equilibria where firms act according to a list of preferences. Moreover, every such equilibrium preserves stability for a particular profile of preferences. In particular, when firms act truthfully, every outcome is stable for the true preferences. Conversely, when the initial matching is the empty matching, every stable matching can be reached as the outcome of an ordinal equilibrium play of the game. |
| Keywords: | Matching Markets; Stability; Random Mechanisms. |
| JEL: | C78 J44 |
| URL: | http://d.repec.org/n?u=RePEc:ise:isegwp:wp122006&r=gth |
| By: | J. Atsu Amegashie |
| Abstract: | In psychological games, higher-order beliefs, emotions, and motives - in addition to actions - affect players’ payoffs. Suppose you are tolerated as opposed to being genuinely accepted by your peers and “friends”. In particular, suppose you are invited to a party, movie, dinner, etc not because your company is desired but because the inviter would feel guilty if she did not invite you. In all of these cases, it is conceivable that the intention behind the action will matter and hence will affect your payoffs. I model intentions in a dynamic psychological game under incomplete information. I find a complex social interaction in this game. In particular, a player may stick to a strategy of accepting every invitation with the goal of discouraging insincere invitations. This may lead one to erroneously infer that this player is eagerly waiting for an invitation, when indeed his behavior is driven more by strategic considerations than by an excessive desire for social acceptance. I discuss how being tolerated but not being truly accepted can explain the rejection of mutually beneficial trades, the choice of identity, social exclusion, marital divorce, and its implication for political correctness and affirmative action. |
| Keywords: | guilt, intentions, psychological game, second-order beliefs, social interaction |
| JEL: | C73 J16 Z13 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_1757&r=gth |
| By: | Claudio Mezzetti; Ilia Tsetlin |
| Abstract: | We study auctions of a single object among symmetric bidders with affiliated values. We show that the second-price auction minimizes revenue among all efficient auction mechanisms in which only the winner pays, and the price only depends on the losers’ bids. In particular, we show that the k-th price auction generates higher revenue than the second-price auction, for all k > 2. It follows that with affiliated private values the k-th price auction yields higher revenue than the English auction. We also show that the k-th price auction may generate higher revenue than the English auction even in a setting with common values. |
| Keywords: | Auctions; Second-Price Auction; English Auction; k-th Price Auction; Affiliated Values; Robust Mechanism Design |
| JEL: | D44 D82 |
| Date: | 2006–07 |
| URL: | http://d.repec.org/n?u=RePEc:lec:leecon:06/8&r=gth |
| By: | Joana Pais |
| Abstract: | We consider centralized matching markets in which, starting from an arbitrary match- ing, frms are successively chosen in a random fashion and offer their positions to the workers they prefer the most. We propose an algorithm that generalizes some well-known algorithms and explore some of its properties. In particular, different executions of the algorithm may lead to different output matchings. We then study incentives in the rev- elation game induced by the algorithm. We prove that ordinal equilibria always exist. Furthermore, every matching that results from an equilibrium play of the game is stable for a particular preference profile. Namely, if an ordinal equilibrium exists in which firms reveal their true preferences, only matchings that are stable for the true preferences can be obtained. |
| Keywords: | Matching Markets; Stability; Random Mechanism. |
| JEL: | C78 J44 |
| URL: | http://d.repec.org/n?u=RePEc:ise:isegwp:wp112006&r=gth |
| By: | Joana Pais |
| Abstract: | In the college admissions problem, we consider the incentives confronting agents who face the prospect of being matched by a random stable mechanism. We provide a fairly complete characterization of ordinal equilbria. Namely, every ordinal equilib- rium yields a degenerate probability distribution. Furthermore, individual rationality is a necessary and sufficient condition for an equilibrium outcome, while stability is guaranteed in ordinal equilibrium where firms act straightforwardly. Finally, we re- late equilibrium behavior in random and in deterministic mechanisms. |
| Keywords: | Matching; College Admissions Problem; Stability; Random Mechanism. |
| JEL: | C78 |
| URL: | http://d.repec.org/n?u=RePEc:ise:isegwp:wp132006&r=gth |
| By: | Helios Herrera; Cesar Martinelli |
| Date: | 2006–07–31 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:321307000000000225&r=gth |
| By: | Rocholl, Jörg |
| Abstract: | This paper examines the results of 93 discriminatory German Treasury auctions between 1998 and 2002. It documents the seller’s use of discretion and its influence on auction outcomes and bidding strategies. The evidence suggests that the seller uses its discretion frequently and substantially. It does not maximize revenues in a single-period game, but moves up in the competitive demand curve to set the auction price close to the market price. Bidders do not make profits in German auctions on average, while their bidding strategies reflect the uncertainty created by the seller’s discretion. The paper extends and tests the multi-unit auction model by Lengwiler (1999). The empirical evidence is consistent with the implication that the market-clearing price depends on the seller’s marginal cost rather than on the submitted demand. |
| Keywords: | Discriminatory auctions, Winner’s curse, Seller discretion |
| JEL: | G28 H63 |
| Date: | 2005 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bubdp1:3374&r=gth |
| By: | Monique Florenzano (Centre d'Economie de la Sorbonne - [CNRS : UMR8174] - [Universit? Panth?on-Sorbonne - Paris I]); Charalambos Aliprantis (Department of Economics, Purdue University - [Purdue University]); Rabee Tourky (Department of Economics, Purdue University - [Purdue University]) |
| Abstract: | Abstract. The second welfare theorem and the core-equivalence theorem have been proved to be fundamental tools for obtaining equilibrium existence theorems, especially in an infinite dimensional setting. For well-behaved exchange economies that we call proper economies, this paper gives (minimal) conditions for supporting with prices Pareto optimal allocations and decentralizing Edgeworth equilibrium allocations as non-trivial equilibria. As we assume neither transitivity nor monotonicity on the preferences of consumers, most of the existing equilibrium existence results are a consequence of our results. A natural application is in Finance, where our conditions lead to new equilibrium existence results, and also explain why some financial economies fail to have equilibrium. |
| Keywords: | Equilibrium; Valuation equilibrium; Pareto-optimum; Edgeworth equilibrium; Properness; ordered topological vector spaces; Riesz-Kantorovich formula; sup-convolution |
| Date: | 2006–07–19 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00086791_v1&r=gth |
| By: | Joana Pais; Ágnes Pintér |
| Abstract: | We present an experimental study where we analyze three well- known matching mechanisms - the Boston, the Gale-Shapley, and the Top Trading Cycles mechanisms - in three different informational set- tings. Our experimental results are consistent with the theory, sug- gesting that the TTC mechanism outperforms both the Boston and the Gale-Shapley mechanisms in terms of efficiency and it is as suc- cessful as the Gale-Shapley mechanism regarding the proportion of truthful preference revelation, whereas manipulation is stronger un- der the Boston mechanism. In addition, even though agents are much more likely to revert to truthtelling in lack of information about the others' payooffs - ignorance may be beneficial in this context - , the TTC mechanism results less sensitive to the amount of information that participants hold. These results therefore suggest that the use of the TTC mechanism in practice is more desirable than of the others. |
| URL: | http://d.repec.org/n?u=RePEc:ise:isegwp:wp142006&r=gth |
| By: | Thibault Gajdos (CREST - Centre de Recherche en Économie et Statistique - [INSEE] - [ École Nationale de la Statistique et de l'Administration Économique]); Jean-Christophe Vergnaud (EUREQUA - Equipe de Recherche en Economie Quantitative - [Université Panthéon-Sorbonne - Paris I]); Jean-Marc Tallon (EUREQUA - Equipe de Recherche en Economie Quantitative - [Université Panthéon-Sorbonne - Paris I]) |
| Abstract: | We develop an axiomatic approach to decision under uncertainty that explicitly takes into account the information available to the decision maker. The information is described by a set of priors and a reference prior. We define a notion of imprecision for this informational setting and show that a decision maker who is averse to information imprecision maximizes the minimum expected utility computed with respect to a subset of the set of initially given priors. The extent to which this set is reduced can be seen as a measure of imprecision aversion. This approach thus allows a lot of flexibility in modelling the decision maker attitude towards imprecision. In contrast, applying<br />Gilboa-Schmeidler [1989] maxmin criterion to the initial set of priors amounts to assuming extreme pessimism. |
| Keywords: | Uncertainty, Decision, Multiple Priors |
| Date: | 2006–07–17 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00086021_v1&r=gth |
| By: | Marco Celentani; Drew Fudenberg; David K Levine; Wolfgang Pesendorfer |
| Date: | 2006–07–31 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:699152000000000019&r=gth |