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on Game Theory |
| By: | Andreas Blume (Department of Economics, University of Pittsburgh); Paul Heidhues (Department of Economics, University of Bonn and CEPR); Jonathan Lafky (Department of Economics, University of Pittsburgh); Johannes Münster (Wissenschaftszentrum Berlin für Sozialforschung (WZB) and Free University of Berlin); Meixia Zhang (Department of Economics, University of Pittsburgh) |
| Abstract: | This paper completely characterizes the set of Nash equilibria of the Vickrey auction for multiple identical units when buyers have non-increasing marginal valuations and there at least three potential buyers. There are two types of equilibria: In the first class of equilibria there are positive bids below the maximum valuation. In this class, above a threshold value all bidders bid truthfully on all units. One of the bidders bids at the threshold for any unit for which his valuation is below the threshold; the other bidders bid zero in this range. In the second class of equilibria there are as many bids at or above the maximum valuation as there are units. The allocation of these bids is arbitrary across bidders. All the remaining bids equal zero. With any positive reserve price equilibrium becomes unique: Bidders bid truthfully on all units for which their valuation exceeds the reserve price. |
| Keywords: | Vickrey auction, Multi-unit auction, ex-post equilibrium, reserve price, uniqueness |
| JEL: | C72 D44 |
| Date: | 2006–06 |
| URL: | http://d.repec.org/n?u=RePEc:trf:wpaper:116&r=gth |
| By: | Elena L. del Mercato (DISES-CSEF, Università degli Studi di Salerno) |
| Abstract: | In pure exchange economies, a poor attention has been given to how the individual consumption possibilities of the members of a coalition should be represented. It seems economically reasonable that our knowledge and our possibility to make decisions depend on the coalition we belong to. We define a coalitional exchange economy by considering a pure exchange economy in which the individual consumption sets of consumers within a coalition depend on the membership of the coalition. Our definition includes as a particular case the classical definition of pure exchange economy. We adapt the core concept to a coalitional exchange economy, and we show the non-emptiness of the core. Finally, we discuss more general setting where individual preferences are also depending on the coalitions. |
| Keywords: | Cooperative game, core, exchange economy, consumption possibility. |
| JEL: | C71 D50 |
| Date: | 2006–05 |
| URL: | http://d.repec.org/n?u=RePEc:mse:wpsorb:b06047&r=gth |
| By: | Wolfgang Leininger |
| Abstract: | It is argued in this paper that the solution concept of an evolutionary stable strategy (ESS) is an adequate analysis tool for contest theory. Moreover, it is shown that in a contest ESS always differs from Nash equilibrium, the hitherto dominant solution concept in contest theory. Finally, an interpretation of finite population ESS contest behavior in terms of Nash behavior is supplied. |
| URL: | http://d.repec.org/n?u=RePEc:mik:wpaper:02_03&r=gth |
| By: | Geoffrey Heal; Howard Kunreuther |
| Abstract: | We model tipping as a game-theoretic phenomenon and investigate the connection between supermodular games, tipping of equilibria and cascading, and apply the results to issues that arise in the context of homeland security and computer security. We show that tipping and cascading can occur in supermodular games and that "increasing differences"is a sufficient condition for tipping. Supermodularity and tipping of equilibria are closely related. We relate our results to Schelling’s early work on tipping. |
| JEL: | C72 D80 H23 |
| Date: | 2006–06 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:12281&r=gth |
| By: | Sam Perlo-Freeman (School of Economics, University of the West of England) |
| Abstract: | The class of simultaneous 2x2 pure-strategy ordinal games (which include well-known games such as Prisoner’s Dilemma, Chicken and Stag Hunt) have received considerable attention, including complete classification schemes by amongst others Rapoport & Guyer (1978) and Robinson & Goforth (2005). This paper focuses on a particularly pertinent subset of these games, described as the ‘Co-operate-Defect’ (C-D) games, which are characterised by each player having a dominant preference for a particular strategy by the other player. These games are therefore relevant in a number of contexts, including arms race games and collective action problems. The C-D games may be efficiently classified by assigning each player one of six distinct types, a classification that cannot be naturally extended to the full class of 2x2 games. The six types and the resulting game forms are analysed, and the subclass of CD games are identified within a topological structure for the 2x2 games devised by Robinson & Goforth (2005). |
| Keywords: | Conflict; co-operation; game theory; co-operate-defect games |
| JEL: | C25 D12 |
| Date: | 2006–06 |
| URL: | http://d.repec.org/n?u=RePEc:uwe:wpaper:0609&r=gth |
| By: | David Cass (Department of Economics, University of Pennsylvania) |
| Abstract: | In this paper I investigate the nature of the beliefs which agents must hold (at least implicitly) in order to justify their considering various alternatives, in two distinct settings: the Walrasian model without production (with competitive equilibrium), and the sell-all version of the Shapley- Shubik market game (with Nash equilibrium). For this purpose I introduce a weak consistency requirement on behavior, one which I refer to as (having) compatible beliefs. My main conclusion is that, in this respect, these two versions of market allocation are essentially identical. For both, contemplating different choices requires varying the associated set of values of the variables defining compatible beliefs. And — though prima facie very different — it turns out that both equilibrium concepts can be recast entirely in terms of having compatible beliefs. My analysis also leads unequivocally to the interesting conclusion that, in the Walrasian model (even elaborated to encompass production, financial markets, and so on), budget constraints must hold, ab initio, with equality. This has one very important consequence: the First Basic Welfare Theorem, as usually stated, is false, as I demonstrate with two distinct counterexamples, the second of which is (in classical terms) unexceptional. |
| Keywords: | general equilibrium, market game, competitive hypothesis, compatible beliefs |
| JEL: | B49 C71 D51 |
| Date: | 2006–06–02 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:06-009&r=gth |
| By: | Stefan Jungcurt (Department of Agricultural Economics and Social Sciences, Humboldt-Universität zu Berlin, Luisenstr. 56, D-10099 Berlin) |
| Abstract: | Functional overlap in the jurisdiction and competencies of international agreements can lead to incomplete and contradicting regulation, which erodes benefits form international cooperation. The framework developed in this paper seeks to further the theoretical analysis of the domestic and international determinants for the origin and the persistence of such incoherence. Using international regulation on the conservation of plant genetic resources as an illustrative example I address two theoretical challenges - the problem of cross-level inference in theories of international cooperation and the differentiation of processes of substantial bargaining from those of negotiated institutional change. Substantial bargains can be formally analyzed as two-level or nested games with variable payoffs, whereas rigorous analysis of institutional change is limited by too many variations in game structure. I use the framework to derive a typology of games for guiding the systematic analysis of the international, domestic and cross-level interactions that may offer explanations for the phenomenon of incoherence due to functional overlap. |
| Date: | 2004–08 |
| URL: | http://d.repec.org/n?u=RePEc:hah:icardp:0204&r=gth |
| By: | Wolfgang Leininger |
| Abstract: | An auction is viewed as a process that in equilibrium generates a binary lottery for each bidder,which the bidder "buys" with his bid. This view allows for a simple way to consistently assess differences in bidding behavior over different bidders and different auctions. E.g. all auctions covered by the Revenue Equivalence Theorem are shown to generate lotteries with identical probabilities, but different pay-offs. It is then argued, that understanding of (experimentally observed) bidding behavior in auctions is enhanced by drawing on the large literature on choice behavior over lotteries. |
| URL: | http://d.repec.org/n?u=RePEc:mik:wpaper:00_06&r=gth |
| By: | Burkhard Hehenkamp |
| Abstract: | This paper shows that, contrary to common conception, robust equilibrium selection is possible in the two-population model of evolution by Kandori, Mailath and Rob (1993). Investigating the class of individualistic adjustment dynamics, we establish that, for generic 2x2 co-ordination games, the evolutionary process always selects the mutation-dominant equilibrium. The concepts of mutation dominance and risk dominance yield different equilibrium predictions, since the concept of mutation dominance additionally captures the systemic risk arising from random matching. |
| URL: | http://d.repec.org/n?u=RePEc:mik:wpaper:01_01&r=gth |
| By: | Ángel Hernando Veciana (Universidad de Alicante) |
| Abstract: | This paper studies the incentives of a bidder to acquire information in anauction when her information acquisition decision is observed by the otherbidders before they bid. Our results show that the sealed bid (second price)auction induces more information acquisition about a common component ofthe value than the open (English) auction, but less about the private componentof the value. Moreover, under our assumptions more information about theprivate value and less information about the common value improves efficiencyand revenue in some sense. Consequently, our results suggest new argumentsin favor of the open auction. |
| Keywords: | auctions, open information acquisition, asymmetric information. |
| JEL: | D41 D44 D82 |
| Date: | 2006–06 |
| URL: | http://d.repec.org/n?u=RePEc:ivi:wpasad:2006-10&r=gth |