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on Game Theory |
| By: | Frank H. Page, Jr. (University of Alabama); Myrna H. Wooders (Vanderbilt University and University of Warwick) |
| Abstract: | We make four main contributions to the theory of network formation. (1) The problem of network formation with farsighted agents can be formulated as an abstract network formation game. (2) In any farsighted network formation game the feasible set of networks contains a unique, finite, disjoint collection of nonempty subsets having the property that each subset forms a strategic basin of attraction. These basins of attraction contain all the networks that are likely to emerge and persist if individuals behave farsightedly in playing the network formation game. (3) A von Neumann Morgenstern stable set of the farsighted network formation game is constructed by selecting one network from each basin of attraction. We refer to any such von Neumann-Morgenstern stable set as a farsighted basis. (4) The core of the farsighted network formation game is constructed by selecting one network from each basin of attraction containing a single network. We call this notion of the core, the farsighted core. We conclude that the farsighted core is nonempty if and only if there exists at least one farsighted basin of attraction containing a single network. To relate our three equilibrium and stability notions (basins of attraction, farsighted basis, and farsighted core) to recent work by Jackson and Wolinsky (1996), we define a notion of pairwise stability similar to the Jackson-Wolinsky notion and we show that the farsighted core is contained in the set of pairwise stable networks. Finally, we introduce, via an example, competitive contracting networks and highlight how the analysis of these networks requires the new features of our network formation model. |
| Keywords: | Basins of attraction, Network formation, Supernetworks, Farsighted core, Nash networks |
| JEL: | A14 D20 J00 |
| Date: | 2005–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2005.36&r=gth |
| By: | Michael Finus (University of Hagen); Pierre v. Mouche (University of Wageningen); Bianca Rundshagen (University of Hagen) |
| Abstract: | We provide an existence and a uniqueness result for coalitional equilibria of a game in strategic form. Both results are illustrated for a public good game and a homogeneous Cournot-oligopoly game. |
| Keywords: | Existence and uniqueness of coalitional equilibrium, Game in strategic form |
| JEL: | C71 |
| Date: | 2005–02 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2005.23&r=gth |
| By: | Vincent Vannetelbosch (CORE, Université Catholique de Louvain); Olivier Tercieux (CentER, Tilburg University) |
| Abstract: | Jackson and Watts [J. of Econ. Theory 71 (2002), 44-74] have examined the dynamic formation and stochastic evolution of networks. We provide a refinement of pairwise stability, p-pairwise stability, which allows us to characterize the stochastically stable networks without requiring the "tree construction" and the computation of resistance that may be quite complex. When a 1/2-pairwise stable network exists, it is unique and it coincides with the unique stochastically stable network. To solve the inexistence problem of p-pairwise stable networks, we define its set-valued extension with the notion of p-pairwise stable set. The 1/2-pairwise stable set exists and is unique. Any stochastically stable network is included in the 1/2-pairwise stable set. Thus, any network outside the 1/2-pairwise stable set must be considered as a nonrobust network. We also show that the 1/2-pairwise stable set can contain no pairwise stable network and we provide examples where a set of networks is more "stable" than a pairwise stable network. |
| Keywords: | Network formation, Pairwise stability, Stochastic stability |
| JEL: | C70 D20 |
| Date: | 2005–04 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2005.48&r=gth |
| By: | Francesco Feri (Ca’ Foscari University) |
| Abstract: | This paper considers a simple communication network characterized by an endogenous architecture and an imperfect transmission of information. We analyze the process of network formation in a dynamic framework where self – interested individuals can form or delete links and, occasionally, are doing mistakes. Then, using stochastic stability, we identify which network structures the formation process will converge to. |
| Keywords: | Network, Decay, Strategical interaction |
| JEL: | A14 D20 J00 |
| Date: | 2005–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2005.40&r=gth |
| By: | Francesco Feri (Ca’ Foscari University) |
| Abstract: | This paper considers a communication network characterized by an endogenous architecture and an imperfect transmission of information as in Bala and Goyal (2000). We propose a similar network's model with the difference that it is characterized by an endogenous rate of information decay. Endogenous decay is modelled as dependent on the result of a coordination game, played by every pair of directly linked agents and characterized by 2 equilibria: one efficient and the other risk dominant. Differently from other models, where the network represents only a channel to obtain information or to play a game, in our paper the network has an intrinsic value that depends on the chosen action in the coordination game by each participant. Moreover the endogenous network structure affects the play in the coordination game as well as the latter affects the network structure. The model has a multiplicity of equilibria and we produce a full characterization of those are stochastically stable. For sufficiently low link costs we find that in stochastically stable states network structure is ever efficient; individuals can be coordinated on efficient as well as on risk dominant action depending on the decay difference among the two equilibria in the single coordination game. For high link costs stochastically stable states can display networks that are not efficient; individuals are never coordinated on the efficient action. |
| Keywords: | Network, Decay, Strategical interaction |
| JEL: | A14 D20 J00 |
| Date: | 2005–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2005.35&r=gth |
| By: | Emmanuel Dechenaux; Dan Kovenock |
| Abstract: | This paper contributes to the study of tacit collusion by analyzing infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under both the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that when each firm sets a price-quantity pair specifying the firm's minimum acceptable price and the maximum quantity the firm is willing to sell at this price, there exists a range of discount factors for which the monopoly outcome with equal sharing is sustainable in the uniform price auction, but not in the corresponding discriminatory auction. Moreover, capacity withholding may be necessary to sustain this out-come. We extend these results to the case where firms may set bids that are arbitrary step functions of price-quantity pairs with any finite number of price steps. Surprisingly, under the Maximum Accepted Price rule, firms need employ no more than two price steps to minimize the value of the discount factor |
| Keywords: | Auction, Capacity, Collusion, Electricity Market, Supply Function |
| JEL: | D43 D44 L13 L41 L94 |
| Date: | 2005–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:645.05&r=gth |
| By: | Antoni Calvó-Armengol (Universitat Autònoma de Barcelona, Université de Toulouse Sciences Sociales and CEPR); Rahmi Ilkiliç (Universitat Autònoma de Barcelona) |
| Abstract: | Suppose that individual payoffs depend on the network connecting them. Consider the following simultaneous move game of network formation: players announce independently the links they wish to form, and links are formed only under mutual consent. We provide necessary and sufficient conditions on the network link marginal payoffs such that the set of pairwise stable, pairwise-Nash and proper equilibrium networks coincide, where pairwise stable networks are robust to one-link deviations, while pairwise-Nash networks are robust to one-link creation but multi-link severance. Under these conditions, proper equilibria in pure strategies are fully characterized by one-link deviation checks. |
| Keywords: | Network formation, Pairwise-stability, Proper equilibrium |
| JEL: | C62 C72 D85 L14 |
| Date: | 2005–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2005.34&r=gth |
| By: | Somdeb Lahiri (University of the Witwatersrand at Johannesburg) |
| Abstract: | This paper proves the existence of non-empty cores for directed network problems with quotas and for those combinatorial allocation problems which permit only exclusive allocations. |
| Keywords: | Network problems, Quotas |
| JEL: | C71 |
| Date: | 2005–02 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2005.25&r=gth |
| By: | Aart de Zeeuw (Tilburg University) |
| Abstract: | In terms of the number of signatories, one observes both large and small international environmental agreements. The theoretical literature, based on game theory, discusses different concepts and mechanisms for the stability of coalitions and has reached the conclusion that, under farsightedness, both large and small stable coalitions can occur. In the context of a repeated game, this implies that large stable coalitions can also be sustained over time by a simple trigger mechanism, for large enough discount factors. However, if changes in time implement changes in state, this conclusion does not hold anymore: only small stable coalitions can be sustained. |
| Keywords: | IEA’s, Coalitional stability, Dynamics |
| JEL: | Q2 C70 F42 |
| Date: | 2005–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2005.41&r=gth |
| By: | Matthew O. Jackson (Humanities and Social Sciences); Alison Watts (Southern Illinois University) |
| Abstract: | We examine a new class of games, which we call social games, where players not only choose strategies but also choose with whom they play. A group of players who are dissatisfied with the play of their current partners can join together and play a new equilibrium. This imposes new refinements on equilibrium play, where play depends on the relative populations of players in different roles, among other things. We also examine finite repetitions of games where players may choose to rematch in any period. Some equilibria of fixed-player repeated games cannot be sustained as equilibria in a repeated social game. Conversely, the set of repeated matching (or social) equilibria also includes some plays that are not part of any subgame perfect equilibrium of the corresponding fixed-player repeated games. We explore existence under different equilibrium definitions, as well as the relationship to renegotiation-proof equilibrium. It is possible for repeated matching equilibria to be completely distinct from renegotiation-proof equilibria, and even to be Pareto inefficient. |
| Keywords: | Social games, Matching, Games, Repeated games, Renegotiation |
| JEL: | A14 C71 C72 C78 J41 |
| Date: | 2005–03 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2005.38&r=gth |
| By: | Carlo Carraro (University of Venice, Fondazione Eni Enrico Mattei, CEPR and CEPS); Barbara Buchner (Fondazione Eni Enrico Mattei) |
| Abstract: | No international regime on climate change is going to be fully effective in controlling GHG emissions without the involvement of countries such as China, India, the United States, Australia, and possibly other developing countries. This highlights an unambiguous weakness of the Kyoto Protocol, where the aforementioned countries either have no binding emission targets or have decided not to comply with their targets. Therefore, when discussing possible post-Kyoto scenarios, it is crucial to prioritise participation incentives for all countries, especially those without explicit or with insufficient abatement targets. This paper offers a bottom-up game-theoretic perspective on participation incentives. Rather than focusing on issue linkage, transfers or burden sharing as tools to enhance the incentives to participate in a climate agreement, this paper aims at exploring whether a different policy approach could lead more countries to adopt effective climate control policies. This policy approach is explicitly bottom-up, namely it gives each country the freedom to sign agreements and deals, bilaterally or multilaterally, with other countries, without being constrained by any global protocol or convention. This study provides a game-theoretic assessment of this policy approach and then evaluates empirically the possible endogenous emergence of single or multiple climate coalitions. Welfare and technological consequences of different multiple bloc climate regimes will be assessed and their overall environmental effectiveness will be discussed. |
| Keywords: | Agreements, Climate, Incentives, Negotiations, Policy |
| JEL: | C72 H23 Q25 Q28 |
| Date: | 2005–02 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2005.21&r=gth |
| By: | Dmitry Ryvkin |
| Abstract: | An elimination tournament matches players pairwise and promotes the winners to a subsequent round where the procedure is repeated. In the presence of idiosyncratic noise the tournament turns into a probabilistic mechanism that reveals the ranking of players imperfectly. I assess theoretically the power of such a mechanism to determine the ex ante best player as the winner, as a function of the number of players, their distribution of type, and the noise level. I consider also various seeding strategies and show that for large and small noise (as compared to the variance of ability distribution among players), seeding and other control parameters of tournament design tend to play no role, whereas for intermediate noise level the predictive power depends strongly on the control parameters and therefore can be systematically manipulated by the principal. |
| Keywords: | Elimination tournaments, Noise, Seeding, Ability distributions, Design economics. |
| JEL: | C73 C90 D21 |
| Date: | 2005–03 |
| URL: | http://d.repec.org/n?u=RePEc:cer:papers:wp252&r=gth |
| By: | Pierpaolo Battigalli; Martin Dufwenberg |
| Abstract: | Building on recent work on dynamic interactive epistemology, we extend the analysis of extensive-form psychological games (Geneakoplos, Pearce & Stacchetti, Games and Economic Behavior, 1989) to include conditional higher-order beliefs and enlarged domains of payoff functions. The approach allows modeling dynamic psychological effects (such as sequential reciprocity, psychological forward induction, and regret) that are ruled out when epistemic types are identified with hierarchies of initial beliefs. We define a notion of psychological sequential equilibrium, which generalizes the sequential equilibrium notion for traditional games, for which we prove existence under mild assumptions. Our framework also allows us to directly formulate assumptions about ‘dynamic’ rationality and interactive beliefs in order to explore strategic interaction without assuming that players beliefs are coordinated on an equilibrium. In particular, we provide an exploration of (extensive-form) rationalizability in psychological games. |
| URL: | http://d.repec.org/n?u=RePEc:igi:igierp:287&r=gth |