nep-gth New Economics Papers
on Game Theory
Issue of 2015‒02‒05
nine papers chosen by
László Á. Kóczy
Magyar Tudományos Akadémia

  1. Bidding Rings: A Bargaining Approach By Chatterjee, Kalyan; Mitra, Manipushpak; Mukherjee, Conan
  2. Equilibrium and matching under price controls By Herings P.J.J.
  3. From bilateral two-way to unilateral one-way flow link-formation By Valenciano Llovera, Federico; Olaizola Ortega, Norma
  4. The art of brevity By Ricardo Alonso; Heikki Rantakari
  5. Unilateral vs. Bilateral link-formation: Bridging the gap By Valenciano Llobera, Federico; Olaizola Ortega, María Norma
  6. Cascading to Equilibrium: Hydraulic Computation of Equilibria in Resource Selection Games By Yannai A. Gonczarowski; Moshe Tennenholtz
  7. Network Formation and Systemic Risk, Second Version By Selman Erol; Rakesh Vohra
  8. Plausible Cooperation, Fourth Version By Oliver Compte; Andrew Postlewaite
  9. Responsive Affirmative Action in School Choice By Battal Dogan

  1. By: Chatterjee, Kalyan (Department of Economics, Pennsylvania State University); Mitra, Manipushpak (Economic Research Unit, Indian Statistical Institute, Kolkata, India); Mukherjee, Conan (Department of Economics, Lund University)
    Abstract: We address the issue of bidder ring formation in single and multi-unit Vickrey auctions. We address this issue in a bargaining game set up under the assumption that valuation of bidders is commonly known only amongst themselves. In the single unit case, we show that the equilibrium coalition structure can only be an order preserving r-ring, that includes the winner and the top (r-1) losers. In the multiple units case, we specify sufficient conditions for formation of an interesting class of equilibrium coalition structures, which we call single winner ring with free riding, where exactly one winner colludes with all the losers and generates maximum possible bidders' surplus, and, depending on the protocol, the remaining winners free ride either by staying alone or by colluding in pairs.
    Keywords: Bidding rings; Bargaining games; Coalition formation; Auctions
    JEL: C71 C72 C78 D44 L41
    Date: 2015–01–16
  2. By: Herings P.J.J. (GSBE)
    Abstract: The paper considers a one-to-one matching with contracts model in the presence of price controls. This set-up contains two important streams in the matching literature, those with and those without monetary transfers, as special cases and allows for intermediate cases with some restrictions on the monetary transfers that are feasible. An adjustment process that ends with a stable outcome is presented, thereby proving the existence of stable outcomes. The process contains the deferred acceptance algorithm of Gale and Shapley 1962 and the approximate auction mechanism of Demange, Gale, and Sotomayor 1986 as special cases. The paper presents a notion of competitive equilibrium, called Drze equilibrium, for this class of models, an extension of the concept as developed by Drze 1975 for economies with divisible commodities subject to price controls. It is shown that Drze equilibrium allocations are equivalent to allocations induced by stable outcomes. One implication is the existence of Drze equilibria. Another implication is the equivalence of a competitive equilibrium concept and the concept of stable outcomes that is valid with and with- out monetary transfers as well as when monetary transfers are limited.
    Keywords: Cooperative Games; Bargaining Theory; Matching Theory; Rationing; Licensing; Exchange and Production Economies;
    JEL: C71 C78 D45 D51
    Date: 2015
  3. By: Valenciano Llovera, Federico; Olaizola Ortega, Norma
    Keywords: network formation, unilateral link-formation, bilateral link-formation, stability, efficiency, dynamics
    JEL: A14 C72 D20 J00
    Date: 2014–11–26
  4. By: Ricardo Alonso; Heikki Rantakari
    Abstract: We analyze a class of sender-receiver games with quadratic payoffs, which includes the communication games in Alonso, Dessein and Matouschek (2008) and Rantakari (2008) as special cases, for which the receiver's maximum expected payoff when players have access to arbitrary, mediated communication protocols is attained in one-round of face-to-face, unmediated cheap talk. This result is based on the existence for these games of a communication equilibrium with an infinite number of partitions of the state space. We provide explicit expressions for the maximum expected payoff of the receiver, and illustrate its use by deriving new comparative statics of the quality of optimal communication. For instance, a shift in the underlying uncertainty that reduces expected conflict can worsen the quality of communication.
    Keywords: communication equilibrium; information transmission; mediation; one-shot cheap talk
    JEL: C72 D70 D83
    Date: 2014–07–31
  5. By: Valenciano Llobera, Federico; Olaizola Ortega, María Norma
    Abstract: We provide a model that bridges the gap between two benchmark models of strategic network formation: Jackson and Wolinsky' s model based on bilateral formation of links, and Bala and Goyal's two-way fl ow model, where links can be unilaterally formed. In the model introduced and studied here a link can be created unilaterally. When it is only supported by one of the two players the fl ow through the link suffers a certain decay, but when it is supported by both the fl ow runs without friction. When the decay in links supported by only one player is maximal (i.e. there is no flow) we have Jackson and Wolinsky 's connections model without decay, while when flow in such links is perfect we have Bala and Goyal' s two-way flow model. We study Nash, strict Nash and pairwise stability for the intermediate models. Efficiency and dynamics are also examined.
    Keywords: network formation, unilateral link-formation, bilateral link-formation, stability, efficiency, dynamics
    JEL: J00 D20 A14 C72
    Date: 2014–05–28
  6. By: Yannai A. Gonczarowski; Moshe Tennenholtz
    Abstract: Drawing intuition from a (physical) hydraulic system, we present a novel framework, constructively showing the existence of a strong Nash equilibrium in resource selection games with nonatomic players, the coincidence of strong equilibria and Nash equilibria in such games, and the invariance of the cost of each given resource across all Nash equilibria. Our proofs allow for explicit calculation of Nash equilibrium and for explicit and direct calculation of the resulting (invariant) costs of resources, and do not hinge on any fixed-point theorem, on the Minimax theorem or any equivalent result, on the existence of a potential, or on linear programming. A generalization of resource selection games, called resource selection games with I.D.-dependent weighting, is defined, and the results are extended to this family, showing that while resource costs are no longer invariant across Nash equilibria in games of this family, they are nonetheless invariant across all strong Nash equilibria, drawing a novel fundamental connection between group deviation and I.D.-congestion. A natural application of the resulting machinery to a large class of constraint-satisfaction problems is also described.
    Date: 2014–12
  7. By: Selman Erol (Department of Economics, University of Pennsylvania); Rakesh Vohra (Department of Economics, and Department of Electrical & Systems Engineering, University of Pennsylvania)
    Abstract: This paper introduces a model of endogenous network formation and systemic risk. In it, strategic agents form networks that efficiently trade-off the possibility of systemic risk with the benefits of trade. Efficiency is a consequence of the high risk of contagion which forces agents to endogenize their externalities. Second, fundamentally ‘safer’ economies generate much higher interconnectedness, which in turn leads to higher systemic risk. Third, the structure of the network formed depends crucially on whether the shocks to the system are believed to be correlated or independent of each other. This underlines the importance of specifying the shock structure before investigating a given network as a particular network and shock structure could be incompatible.
    Keywords: Network Formation, Systemic Risk, Contagion, Rationalizability, Core
    JEL: D85 G01
    Date: 2014–08–29
  8. By: Oliver Compte (Paris School of Economics); Andrew Postlewaite (Department of Economics, University of Pennsylvania)
    Abstract: There is a large repeated games literature illustrating how future interactions provide incentives for cooperation. Much of the earlier literature assumes public monitoring. Departures from public monitoring to private monitoring that incorporate differences in players’ observations may dramatically complicate coordination and the provision of incentives, with the consequence that equilibria with private monitoring often seem unrealistically complex or fragile. We set out a model in which players accomplish cooperation in an intuitively plausible fashion. Players process information via a mental system — a set of psychological states and a transition function between states depending on observations. Players restrict attention to a relatively small set of simple strategies, and consequently, might learn which perform well.
    Keywords: : repeated games, private monitoring, bounded rationality, cooperation
    JEL: D01 D70
    Date: 2010–12–01
  9. By: Battal Dogan
    Abstract: School choice programs aim to give students the option to choose their school. At the same time, underrepresented minority students should be favored to close the opportunity gap. A common way to achieve this is to have a majority quota at each school, and to require that no school be assigned more majority students than its majority quota. An alternative way is to reserve some seats at each school for the minority students, and to require that a reserve seat at a school be assigned to a majority student only if no minority student prefers that school to her assignment. However, fair rules based on either type of affirmative action suffer from a common problem: a stronger affirmative action may not benefit any minority student and hurt some minority students. First, we show that this problem is pervasive: the problem disappears only if the minority students "mostly" have priority over the majority students. Then, we uncover the root of this problem: for some minority students, treating them as minority students does not benefit them, but possibly hurts other minority students. We propose a new assignment rule (Modified deferred acceptance with minority reserves), which treats such minority students as majority students, achieves affirmative action, and never hurts a minority student without benefiting another minority student.
    Keywords: school choice; affirmative action; minimal responsiveness
    JEL: C78 D71 D78
    Date: 2015–01

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