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on Game Theory |
| By: | Kuipers, Jeroen (MICC-Mathematics, Maastricht University, the Netherlands); Vermeulen, Dries (Department of Quantitative Economics, Maastricht University, the Netherlands); Voorneveld, Mark (Dept. of Economics, Stockholm School of Economics) |
| Abstract: | The Shapley-Ichiishi result states that a game is convex if and only if the convex hull of marginal vectors equals the core. In this paper we generalize this result by distinguishing equivalence classes of balanced games that share the same core structure. We then associate a system of linear inequalities with each equivalence class, and we show that the system defines the class. Application of this general theorem to the class of convex games yields an alternative proof of the Shapley-Ichiishi result. Other applications range from computation of stable sets in non-cooperative game theory to determination of classes of TU games on which the core correspondence is additive (even linear). For the case of convex games we prove that the theorem provides the minimal defining system of linear inequalities. An example shows that this is not necessarily true for other equivalence classes of balanced games. |
| Keywords: | cooperative games; Shapley-Ichiishi; balanced games; core |
| JEL: | C71 |
| Date: | 2009–03–03 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:hastef:0711&r=gth |
| By: | Mengel Friederike; Tsakas Elias; Vostroknutov Alexander (METEOR) |
| Abstract: | In this paper we provide a framework to reason about limited awareness of the action space in finitely repeated games. Our framework is rich enough to capture the full strategic aspect of limited awareness in a dynamic setting, taking into account the possibility that agents might want to reveal or conceal actions to their opponent or that they might become "aware of unawareness" upon observing non rationalizable behavior. We show that one can think of these situations as a game with incomplete information, which is fundamentally different, though, from the standard treatment of repeated games with incomplete information. We establish conditions on the "level of mutual awareness" of the action space needed to recover Nash and subgame perfect Nash equilibria from the standard theory with common knowledge. We also show that the set of sustainable payoffs in games with folk theorems does not relate in a monotone way to the "level of mutual awareness". |
| Keywords: | mathematical economics; |
| Date: | 2009 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2009010&r=gth |
| By: | Ganna Pogrebna; Pavlo Blavatskyy |
| Abstract: | This paper studies coordination in a multi-stage elimination tournament with large monetary incentives and a diversified subject pool drawn from the adult British population. In the tournament, members of an ad hoc team earn money by answering general knowledge questions and then eliminate one contestant by plurality voting without prior communication. We find that in the early rounds of the tournament, contestants use a focal principle and coordinate on one of the multiple Nash equilibria in pure strategies by eliminating the weakest member of the team. However, in the later rounds, contestants switch to playing a mixed strategy Nash equilibrium. |
| Keywords: | Coordination, focal point, voting in strategic situations |
| JEL: | C72 C93 D72 |
| Date: | 2009–02 |
| URL: | http://d.repec.org/n?u=RePEc:zur:iewwpx:403&r=gth |
| By: | In-Koo Cho; Akihiko Matsui |
| Date: | 2009–02–21 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:814577000000000134&r=gth |
| By: | Nagore Iriberri; Pedro Rey-Biel |
| Abstract: | We compare behavior in modified dictator games with and without role uncertainty. Costly surplus creating actions are most frequent with role uncertainty while selfish behavior is most frequent without role uncertainty. A classification of subjects into four different types of preferences (Selfish, Social Welfare maximizing, Inequity Averse and Competitive) shows that role uncertainty overestimates (underestimates) the prevalence of Social Welfare maximizing (Selfish and Inequity Averse) preferences in the subject population. Our results have important methodological implications for experiments used to measure the prevalence of interdependent preferences. |
| Keywords: | Role uncertainty, role reversal, interdependent preferences, social welfare, maximizing, inequity aversion, mixture-of-types models, strategy method, experiments, LeeX |
| JEL: | C72 C91 D81 |
| Date: | 2008–05 |
| URL: | http://d.repec.org/n?u=RePEc:upf:upfgen:1147&r=gth |
| By: | Tasnádi, Attila |
| Abstract: | We consider a possible game-theoretic foundation of Forchheimer's model of dominant-firm price leadership based on quantity-setting games with one large firm and many small firms. If the large firm is the exogenously given first mover, we obtain Forchheimer's model. We also investigate whether the large firm can emerge as a first mover of a timing game. |
| Keywords: | Forchheimer; Dominant firm; Price leadership |
| JEL: | L13 D43 |
| Date: | 2009–02–24 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:13612&r=gth |
| By: | Jeremy Bulow; Jonathan Levin; Paul Milgrom |
| Abstract: | We describe factors that make bidding in large spectrum auctions complex -- including exposure and budget problems, the role of timing within an ascending auction, and the possibilities for price forecasting -- and how economic and game-theoretic analysis can assist bidders in overcoming these problems. We illustrate with the case of the FCC's Advanced Wireless Service auction, in which a new entrant, SpectrumCo, faced all these problems yet managed to purchase nationwide coverage at a discount of roughly a third relative to the prices paid by its incumbent competitors in the same auction, saving more than a billion dollars. |
| JEL: | C72 D44 L21 |
| Date: | 2009–03 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:14765&r=gth |