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on Game Theory |
| By: | Miguel A. Costa-Gomes; Vincent P. Crawford |
| Date: | 2006–09–02 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:321307000000000336&r=gth |
| By: | Frenk, J.B.G.; Kassay, G. (Erasmus Research Institute of Management (ERIM), RSM Erasmus University) |
| Abstract: | In this chapter we give an overview on the theory of noncooperative games. In the first part we consider in detail for zero-sum (and constant-sum) noncooperative games under which necessary and sufficient conditions on the payoff function and different (extended) strategy sets for both players an equilibrium saddlepoint exists. This is done by using the most elementary proofs. One proof uses the separation result for disjoint convex sets, while the other proof uses linear programming duality and some elementary properties of compact sets. Also, for the most famous saddlepoint result given by Sion's minmax theorem an elementary proof using only the definition of connectedness is given. In the final part we consider n-person nonzero-sum noncooperative games and show by a simple application of the KKM lemma that a so-called Nash equilibrium point exists for compact strategy sets and concavity conditions on the payoff functions. |
| Keywords: | Non-Cooperative Game Theory;Minimax Theorems;Nash Equilibrium Point;KKM Lemma;Equilibrium Problems; |
| Date: | 2006–06–10 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:eureri:30008715&r=gth |
| By: | Michihiro Kandori; Ichiro Obara |
| Date: | 2006–09–02 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:321307000000000342&r=gth |
| By: | Engelbert J. Dockner (University of Vienna, Austria); Florian O.O. Wagener (CeNDEF, Universiteit van Amsterdam) |
| Abstract: | Many economic problems can be formulated as dynamic games in which strategically interacting agents choose actions that determine the current and future levels of a single capital stock. We study necessary conditions that allow us to characterize Markov perfect Nash equilibria (MPNE) for these games. These conditions result in an auxiliary system of ordinary differential equations that helps us to explore stability, continuity and differentiability of MPNE. The techniques are used to derive detailed properties of MPNE for several games including the exploitation of a finite resource, the voluntary investment in a public capital stock, and the inter-temporal consumption of a reproductive asset. |
| Keywords: | Capital accumulation games; Markov equilibria; Resource games; Differential games |
| JEL: | C73 D92 Q22 |
| Date: | 2006–06–22 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20060055&r=gth |
| By: | Dequiedt, V. |
| Abstract: | The note points out some restrictions imposed by the notion of ratification. This notion is widely used in the mechanism design literature that assumes that each agent has a veto power. We exhibit allocations that are note ratifiable and nevertheless can be implemented through a mechanism that gives veto power to the agents. |
| Keywords: | MECHANISM DESIGN; PARTICIPATION CONSTRAINTS; RATIFIABILITY; VETO |
| JEL: | C72 D78 D82 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:gbl:wpaper:200606&r=gth |
| By: | Dequiedt, V. |
| Abstract: | We study collusion in an IPV auction with binary type spaces. Collusion is organized by a third-party than can manipulate participation decisions. We characterize the optimal response of the seller to different threats of collusion among the bidders. We show that, contrary to the prevailing view that assymmetric information imposes transaction costs in side-contracting, collusion in the optimal auction is efficient when the third-party can implement monetary transfers as well as when it can implement monetary transfers and reallocations of the good. The threat of non-participation in the auction by a subset of bidders is crucial in constraining the seller's profit. |
| Keywords: | COLLUSION; THIRD PARTY; OPTIMAL AUCTION |
| JEL: | D82 |
| Date: | 2006 |
| URL: | http://d.repec.org/n?u=RePEc:gbl:wpaper:200607&r=gth |
| By: | René van den Brink (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam) |
| Abstract: | Many economic organizations have some relational structure, meaning that economic agents do not only differ with respect to certain individual characteristics such as wealth and preferences, but also belong to some relational structure in which they usually take different positions. Two examples of such structures are communication networks and hierarchies. In the literature the distinction between these two types of relational structures is not always clear. In models of restricted cooperation this distinction should be defined by properties of the set of feasible coalitions. We characterize the feasible sets in communication networks and compare them with feasible sets arising from hierarchies. |
| Keywords: | communication; hierarchy; cooperative game; feasible set |
| JEL: | C71 D85 |
| Date: | 2006–07–03 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20060056&r=gth |