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on Game Theory |
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Issue of 2013‒01‒19
ten papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Feinberg, Yossi (Stanford University) |
| Abstract: | We provide a tool to model and solve strategic situations where players' perceptions are limited, in the sense that they may only be aware of, or model, some of the aspects of the strategic situations at hand, as well as situations where players realize that other players' perceptions may be limited. We define normal, repeated, incomplete information and dynamic (extensive) form games with unawareness using a unified methodology. A game with unawareness is defined as a collection of standard games (of the corresponding form). The collection specifies how each player views the game, how she views the other players' perceptions of the game and so on. The modeler's description of perceptions, the players' description of other players' reasoning, etc. are shown to have consistent representations. We extend solution concepts such as rationalizability and Nash equilibrium to these games and study their properties. It is shown that while unawareness in normal form games can be mapped to incomplete information games, the extended Nash equilibrium solution is not mapped to a known solution concept in the equivalent incomplete information games, implying that games with unawareness generate novel types of behavior. |
| JEL: | C72 D81 D82 |
| Date: | 2012–08 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:2122&r=gth |
| By: | Lindgren, Kristian; Verendel, Vilhelm |
| Abstract: | The finitely repeated Prisoners' Dilemma is a good illustration of the discrepancy between the strategic behaviour suggested by a game-theoretic analysis and the behaviour often observed among human players, where cooperation is maintained through most of the game. A game-theoretic reasoning based on backward induction eliminates strategies step by step until defection from the first round is the only remaining choice, reflecting the Nash equilibrium of the game. We investigate the Nash equilibrium solution for two different sets of strategies in an evolutionary context, using replicator-mutation dynamics. The first set consists of conditional cooperators, up to a certain round, while the second set in addition to these contains two strategy types that react differently on the first round action: The "Convincer" strategies insist with two rounds of initial cooperation, trying to establish more cooperative play in the game, while the "Follower" strategies, although being first round defectors, have the capability to respond to an invite in the first round. For both of these strategy sets, iterated elimination of strategies shows that the only Nash equilibria are given by defection from the first round. We show that the evolutionary dynamics of the first set is always characterised by a stable fixed point, corresponding to the Nash equilibrium, if the mutation rate is sufficiently small (but still positive). The second strategy set is numerically investigated, and we find that there are regions of parameter space where fixed points become unstable and the dynamics exhibits cycles of different strategy compositions. The results indicate that, even in the limit of very small mutation rate, the replicator-mutation dynamics does not necessarily bring the system with Convincers and Followers to the fixed point corresponding to the Nash equilibrium of the game. We also perform a detailed analysis of how the evolutionary behaviour depends on payoffs, game length, and mutation rate. |
| Keywords: | backward induction; rationality; prisoners' dilemma; evolutionary dynamics |
| JEL: | C7 C73 C72 |
| Date: | 2013–01–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:43662&r=gth |
| By: | Manfred Kerber; Colin Rowat |
| Abstract: | Pillage games [Jordan, 2006, "Pillage and Property", JET] have two features that make them richer than cooperative games in either characteristic or partition function form: they allow power externalities between coalitions; they allow resources to contribute to coalitions' power as well as to their utility. Extending von Neumann and Morgenstern's analysis of three agent games in characteristic function form to anonymous pillage games, we find: when the core is non-empty, it must take one of five forms; all such games with an empty core represent the same dominance relation. When a stable set exists, and the game also satisfies a continuity and a responsiveness axiom, it is unique and contains no more than 15 elements, a tight bound. By contrast, stable sets in three agent games in characteristic or partition function form may not be unique, and may contain continua. Finally, we provide an algorithm for computing the stable set, and can easily decide non-existence. Thus, in addition to offering attractive modelling possibilities, pillage games seem well behaved and analytically tractable, overcoming a difficulty that has long impeded use of cooperative game theory's flexibility. |
| Keywords: | co-operative game theory, stable sets, algorithm, core |
| JEL: | C63 C71 P14 |
| Date: | 2012–11 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:12-11&r=gth |
| By: | Roman M. Sheremeta (Argyros School of Business and Economics, Chapman University); Jingjing Zhang (University of Zurich) |
| Abstract: | We examine behavior in a three-player trust game in which the first player may invest in the second and the second may invest in the third. Any amount sent from one player to the next is tripled. The third player decides the final allocation among three players. The baseline treatment with no communication shows that the first and second players send significant amounts and the third player reciprocates. Allowing insider communication between the second and the third players increases cooperation between these two. Interestingly, there is an external effect of insider communication: the first player who is outside communication sends 54% more and receives 289% more than in the baseline treatment. As a result, insider communication increases efficiency from 44% to 68%. |
| Keywords: | three-player trust games, experiments, reciprocity, communication |
| JEL: | C72 C91 D72 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:13-03&r=gth |
| By: | Miquel Oliu-Barton (C&O - Equipe combinatoire et optimisation - Université Paris VI - Pierre et Marie Curie - CNRS : FRE3232) |
| Abstract: | We provide a direct, self-contained proof for the existence of the limit, as λ→0, of the values of a λ-discounted finite two-person zero-sum stochastic game. |
| Keywords: | stochastic game; asymptotic value; |
| Date: | 2012–12–19 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-00772631&r=gth |
| By: | Pascal Billand (Université de Lyon, Lyon, F-69007, France ; CNRS, GATE Lyon St Etienne,F-69130 Ecully, France ; Université Jean Monnet, Saint-Etienne, F-42000, France.); Christophe Bravard (Université Grenoble 2 ; UMR 1215 GAEL, F-38000 Grenoble, France ; CNRS, GATE Lyon St Etienne, Saint-Etienne, F-42000, France); Marie Sudipta Sarangi (DIW Berlin and Louisiana State University) |
| Abstract: | We study the formation of mutual insurance networks in a model where every agent who obtains more resources gives a fixed amount of resources to all agents who have obtained less resources. The low resource agent must be directly linked to the high resource agent to receive this transfer. We identify the pairwise stable networks and efficient networks. Then, we extend our model to situations where agents differ in their generosity with regard to the transfer scheme. We show that there exist conditions under which in a pairwise stable network agents who provide the same level of transfers are linked together, while there are no links between agents who provide high transfers and agents who provide low transfers. |
| Keywords: | Mutual insurance networks, Pairwise stable networks, Efficient networks |
| JEL: | C72 D81 D8 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:1234&r=gth |
| By: | Feinberg, Yossi (Stanford University); Kets, Willemien (Northwestern University) |
| Abstract: | We investigate the scope for cooperation within a community engaged in repeated reciprocal interactions. Players seek the help of others and approach them sequentially according to some fixed order, that is, a ranking profile. We study the ranking profiles that are most effective in sustaining cooperation in equilibrium, that is, profiles that support full cooperation in equilibrium under the largest set of parameters. These are the profiles that spread the costs of helping others equally among the members of the community. We show that, generically, these socially optimal ranking profiles correspond to Latin squares--profiles in which each player appears in a given position exactly once in other players' list. In addition, we study equilibria with bilateral enforcement in which only the victims punish non-cooperating deviators. We show that the Latin squares in which every two players rank each other at the same position can sustain cooperation for the widest range of parameters in this case. |
| Date: | 2012–12 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:stabus:2127&r=gth |
| By: | Wolfgang Buchholz (Department of Economics, University of Regensburg); Richard Cornes; Dirk Rübbelke |
| Abstract: | Recent international climate negotiations suggest that complete agreements are unlikely to materialize. Instead, partial cooperation between like-minded countries appears a more likely outcome. In this paper we analyze the effects of such partial cooperation between like-minded countries. In doing so, we link the literature on partial cooperation with so-called matching approaches. Matching schemes are regarded as providing a promising approach to overcome undersupply of public goods like climate protection. The functioning of matching mechanisms in a setting with an incomplete agreement, i.e. a contract where only a subset of the players participates, has however not been investigated yet. This paper fills this research gap by analyzing incomplete matching agreements in the context of international climate protection. We analyse their effect on both welfare and the global climate protection level. We show that matching coalitions may bring about a decline in global public good provision and a reduction in the welfare of outsiders. |
| Keywords: | Coalition formation, public goods, matching, Pareto optimality, partial cooperation |
| JEL: | C78 H41 Q54 |
| Date: | 2012–07 |
| URL: | http://d.repec.org/n?u=RePEc:euv:dpaper:005&r=gth |
| By: | Clemens Heuson; Wolfgang Peters (Faculty of Business Administration and Economics, European University Viadrina, Frankfurt (Oder)); Reimund Schwarze; Anna-Katharina Topp (Faculty of Business Administration and Economics, European University Viadrina, Frankfurt (Oder)) |
| Abstract: | Funding developing countries’ climate policies after Cancun (COP16) has a dual goal: firstly, to support mitigation of developing countries in order to sustain the two-degree pathway of stabilising the global mean temperature; secondly, to empower the vulnerable countries in lowincome regions to adapt to and recover from the most adverse impacts of climate change. So far, the political and scientific discussion has mainly concentrated on the appropriate level of funding. Referring to the newly emerging climate finance architecture under the post-Kyoto framework, this paper argues that a stronger focus must be put on the question: which mode of funding to choose? This is for the reason that the currently discussed funding instruments, such as earmarking of industrialised countries’ transfer payments to developing countries for reducing loss and damages, mitigation, or adaptation costs, may cause fundamental changes in the countries’ strategic behaviour concerning mitigation and adaptation efforts. Moreover, some of the instruments fall short of a minimum requirement for the donors to voluntarily provide means, and thus cannot guarantee sustained funding. We develop our results in a non-cooperative two-country framework in which donor and recipient decide on mitigation in the first, and on adaptation in the second stage of the game. |
| Keywords: | adaptation, climate policy, funding, mitigation, non-cooperative behaviour |
| JEL: | C72 D61 F35 Q54 |
| Date: | 2012–07 |
| URL: | http://d.repec.org/n?u=RePEc:euv:dpaper:004&r=gth |
| By: | Matthias Messner; Nicola Pavoni; Christopher Sleet |
| Abstract: | Several recent papers have proposed recursive Lagrangian-basedmethods for solving dynamic contracting problems. Thesemethods give rise to Bellman operators that incorporate either a dual inf-sup or a saddle point operation. We give conditions that ensure the Bellman operator implied by a dual recursive formulation is contractive. JEL codes: C61, C73, D82, E61. Keywords: Dynamic Contracts, Duality, Dynamic Programming, Contraction Mapping Theorem. |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:igi:igierp:466&r=gth |