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on Game Theory |
| By: | Michal Bresky |
| Abstract: | The paper examines a general class of multi-unit auctions. The class of games investigated includes uniform-price, pay-your-bid, all-pay and Vickrey auctions as special cases. The seller offers k identical units of goods and sets the minimum accepted bid. Bidders have atomless valuation distributions and they submit up to k bids. For this class, the existence of Nash equilibrium in a measurable strategy space and weakly increasing pure strategy space is proven. In many cases any equilibrium strategies can be modified in such a way that they form a pure strategy equilibrium. Properties of standard strategies in multi-unit auctions are analyzed. |
| Keywords: | Multiple-unit auction, existence of equilibrium in discontinuous games, all-pay, pay-your-bid and uniform-price auctions, auctions with reservation price. |
| JEL: | D44 |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:cer:papers:wp376&r=gth |
| By: | Eugen Kovac; Jakub Steiner |
| Abstract: | Agents at the beginning of a dynamic coordination process (1) are uncertain about actions of their fellow players and (2) anticipate receiving strategically relevant information later on in the process. In such environments, the (ir)reversibility of early actions plays an important role in the choice among them. We characterize the strategic eects of the reversibility option on the coordination outcome. Such an option can either enhance or hamper ecient coordination, and we determine the direction of the effect based only on simple features of the coordination problem. The analysis is based on a generalization of the Laplacian property known from static global games: Players at the beginning of a dynamic game act as if they were entirely uninformed about aggregate play of fellow players in each stage of the coordination process. |
| Keywords: | Delay, Exit, Global games, Laplacian belief, Learning, Option, Reversibility. |
| JEL: | C7 D8 |
| Date: | 2008–11 |
| URL: | http://d.repec.org/n?u=RePEc:cer:papers:wp374&r=gth |
| By: | Nicholas Bardsley (National Centre for Research Methods, University of Southampton); Judith Mehta (School of Economics, University of East Anglia); Chris Starmer (CeDEx, University of Nottingham); Robert Sugden (School of Economics, University of East Anglia) |
| Abstract: | This paper reports experimental tests of two alternative explanations of how players use focal points to select equilibria in one-shot coordination games. Cognitive hierarchy theory explains coordination as the result of common beliefs about players’ pre-reflective inclinations towards the relevant strategies; the theory of team reasoning explains it as the result of the players’ using a non-standard form of reasoning. We report two experiments. One finds strong support for team reasoning; the other supports cognitive hierarchy theory. In the light of additional questionnaire evidence, we conclude that players’ reasoning is sensitive to the decision context. |
| Keywords: | salience, focal point, cognitive hierarchy, team reasoning |
| JEL: | C72 C92 |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:cdx:dpaper:2008-17&r=gth |
| By: | Du, Songzi |
| Abstract: | In this note we characterize a refinement of rationalizability with intrinsic correlation introduced in Brandenburger and Friedenberg (2008) in terms of payoffs of the game. The refinement comes from the common knowledge of rationality model of Aumann and Dreze (2008) stripped of redundant types. The characterization is best-response set, which characterizes the usual rationalizability, plus an injectivity condition for a certain subset identified by an iterative procedure. We also give an iterative procedure, analogous to the iterated removals of dominated actions, that arrives at the refinement of rationalizability with intrinsic correlation, which is non-empty in every finite game. |
| Keywords: | game theory; rationalizability; correlation; higher order beliefs; redundant types; epistemics |
| JEL: | C70 C72 |
| Date: | 2008–12–08 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:12592&r=gth |
| By: | Alex Possajennikov (University of Nottingham) |
| Abstract: | The evolutionary stability of payoff-maximizing preferences in the model of indirect evolution in symmetric games depends on the slope of the reaction function being zero at equilibrium. The application of this result to contests confirms that in two-player contests the optimal delegation involves giving the agent incentives to maximize principal's payoff while in contests with more than two players incentives will be different from principal's payoff maximization. Further examples are also discussed. |
| Keywords: | delegation, indirect evolution, contests |
| JEL: | C72 D02 |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:cdx:dpaper:2008-15&r=gth |
| By: | Peters Hans; Roy Souvik; Storcken Ton (METEOR) |
| Abstract: | Under a k-approval scoring rule each agent attaches a score of one to his k most preferred alternatives and zero to the other alternatives. The rule assigns the set of alternatives with maximal score. Agents may extend preferences to sets in several ways: they may compare the worst alternatives, or the best alternatives, or use a stochastic dominance criterion. In this paper we characterize the non-manipulable profiles for each of these set comparisons. For two-agent profiles we also determine the value(s) of k for which the number of non-manipulable profiles is maximal. |
| Keywords: | microeconomics ; |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2008056&r=gth |
| By: | Clayton Featherstone; Muriel Niederle |
| Abstract: | Criteria for evaluating school choice mechanisms are first, whether truth-telling is sometimes punished and second, how efficient the match is. With common knowledge preferences, Deferred Acceptance (DA) dominates the Boston mechanism by the first criterion and is ambiguously ranked by the second. Our laboratory experiments confirm this. A new ex ante perspective, where preferences are private information, introduces new efficiency costs borne by strategy-proof mechanisms, like DA. In a symmetric environment, truth-telling can be an equilibrium under Boston, and Boston can first-order stochastically dominate DA in terms of efficiency, both in theory and in the laboratory. |
| JEL: | C78 C9 I2 |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:14618&r=gth |
| By: | František Turnovec (Institute of Economic Studies, Faculty of Social Sciences, Charles University, Prague, Czech Republic) |
| Abstract: | The concept of fair representation of voters in a committee representing different voters’ groups, such as national representations in union of states, is discussed. This concept, introduced into discussion about voting rights in the Council of European Union in 2004, was narrowed to proposal of distribution of voting weights among the member states proportionally to square roots of population. Such a distribution should guarantee the same indirect voting power to each EU citizen, measured by Penrose-Banzhaf index of voting power. In this paper we attempt to clarify this concept. |
| Keywords: | Council of Ministers, indirect voting power, Penrose-Banzhaf power index, Shapley-Shubik power index, square root rule, simple voting game |
| JEL: | C71 D72 H77 |
| Date: | 2009–01 |
| URL: | http://d.repec.org/n?u=RePEc:fau:wpaper:wp2009_01&r=gth |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Stephen Morris (Dept. of Economics, Princeton University) |
| Abstract: | In a general interdependent preference environment, we characterize when two payoff types can be distinguished by their rationalizable strategic choices without any prior knowledge of their beliefs and higher order beliefs. We show that two payoff types are strategically distinguishable if and only if they satisfy a separability condition. The separability condition for each agent essentially requires that there is not too much interdependence in preferences across agents. A social choice function -- mapping payoff type profiles to outcomes -- can be robustly virtually implemented if there exists a mechanism such that every equilibrium on every type space achieves an outcome arbitrarily close to the social choice function. This definition is equivalent to requiring virtual implementation in iterated deletion of strategies that are strictly dominated for all beliefs. The social choice function is robustly measurable if strategically indistinguishable payoff types receive the same allocation. We show that ex post incentive compatibility and robust measurability are necessary and sufficient for robust virtual implementation. |
| Keywords: | Mechanism design, Virtual implementation, Robust implementation, Rationalizability, Ex-post incentive compatibility |
| JEL: | C79 D82 |
| Date: | 2007–06 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1609rr&r=gth |