nep-mic New Economics Papers
on Microeconomics
Issue of 2012‒07‒23
sixteen papers chosen by
Jing-Yuan Chiou
IMT Lucca Institute for Advanced Studies

  1. The Design of Ambiguous Mechanisms By Alfredo Di Tillio; Nenad Kos; Matthias Messner
  2. What Is a Solution to a Matrix Game By Martin Shubik
  3. Solving Two Sided Incomplete Information Games with Bayesian Iterative Conjectures Approach By Teng, Jimmy
  4. A Unified Approach to Equilibrium Existence in Discontinuous Strategic Games By Philippe Bich; Rida Laraki
  5. Asymmetric Dominance, Deferral and Status Quo Bias in a Theory of Choice with Incomplete Preferences By Gerasimou, Georgios
  6. The Clan and the City: Sustaining Cooperation in China and Europe By Avner Greif; Guido Tabellini
  7. Preserving coalitional rationality for non-balanced games By Stéphane Gonzalez; Michel Grabisch
  8. A Reason for Unreason: Returns-Based Beliefs in Game Theory By Velu, Chander; Iyer, Sriya; Gair, Jonathan R.
  9. What floats your boat? Preference revelation from lotteries over complex goods By Jonathan K. Yoder; Adrienne M. Ohler; Hayley H. Chouinard
  10. Incentives to Motivate By Kvaløy, Ola; Schöttner, Anja
  11. Honesty, lemons, and symbolic signals By Jorge M. Streb; Gustavo Torrens
  12. Bargaining Order in a Multi-Person Bargaining Game By Jun Xiao
  13. Monotonicity, Non-Participation, and Directed Search Equilibria By James Bland, Simon Loertscher
  14. Asymmetric All-Pay Contests with Heterogeneous By Jun Xiao
  15. Duality in Contracting By Peter Bardsley
  16. Learning Nash Equilibria By Dai, Darong

  1. By: Alfredo Di Tillio; Nenad Kos; Matthias Messner
    Abstract: This paper considers the optimal mechanism design problem of an expected revenue maximizing principal who wants to sell a single unit of a good to an agent who is ambiguity averse in the sense of Gilboa and Schmeidler (1989). We show that the optimal static mechanism is an ambiguous mechanism. An ambiguous mechanism specifies a message space and a set of outcome functions. After showing that (a version of) the Revelation Principle holds in our environment, we give an exact characterization of the (smallest) optimal ambiguous mechanism. If the type set is composed of N (finite) types, then the (smallest) optimal ambiguous mechanism contains N - 1 outcome functions. We show that the share of the surplus that the designer can extract from the agent increases as the type set becomes larger and the probability of each single type decreases. In the limiting case where the agent’s type is drawn from a non-atomic distribution on an interval, the optimal ambiguous mechanism extracts all the rent from the agent.
    Date: 2012
  2. By: Martin Shubik (Cowles Foundation, Yale University)
    Abstract: These notes are provided to describe many of the problems encountered concerning both structure and behavior in specifying what is meant by the solution to a game of strategy in matrix or strategic form. In the short term in particular, it is often reasonable for the individual to accept as given, both the context in which decisions are being made and the formal structure of the rules of the game. A solution is usually considered as a complete set of equations of motion that when applied to the game at hand selects a final outcome. There are many different theories and conjectures about how games of strategy are, or should be played. Several of them are noted below. They are especially relevant to the experimental gaming facility noted in the companion paper.
    Keywords: Matrix games, Solution concepts, Experimental gaming
    JEL: C7 C9
    Date: 2012–07
  3. By: Teng, Jimmy
    Abstract: This paper proposes a way to solve two (and multiple) sided incomplete information games which generally generates a unique equilibrium. The approach uses iterative conjectures updated by game theoretic and Bayesian statistical decision theoretic reasoning. Players in the games form conjectures about what other players want to do, starting from first order uninformative conjectures and keep updating with games theoretic and Bayesian statistical decision theoretic reasoning until a convergence of conjectures is achieved. The resulting convergent conjectures and the equilibrium (which is named Bayesian equilibrium by iterative conjectures) they supported form the solution of the game. The paper gives two examples which show that the unique equilibrium generated by this approach is compellingly intuitive and insightful. The paper also solves an example of a three sided incomplete information simultaneous game.
    Keywords: new equilibrium concept; two and multiple sided incomplete information; iterative conjectures; convergence; Bayesian decision theory; Schelling point
    JEL: C70 C72
    Date: 2012–03–01
  4. By: Philippe Bich (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris); Rida Laraki (Ecole Polytechnique - Ecole Polytechnique, IMJ - Institut de Mathématiques de Jussieu - CNRS : UMR7586 - Université Paris VI - Pierre et Marie Curie - Université Paris VII - Paris Diderot)
    Abstract: Several relaxations of Nash equilibrium are shown to exist in strategic games with discontinuous payoff functions. Those relaxations are used to extend and unify several recent results and link Reny's better-reply security condition [Reny, P.J. (1999). On the existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games] to Simon-Zame's endogenous tie-breaking rules [Simon, L.K. and Zame, W.R. (1990). Discontinuous Games and Endogenous Sharing Rules].
    Keywords: Discontinuous games, Nash equilibrium, Reny equilibrium, better-reply security, endogenous sharing rule, quasi equilibrium, finite deviation equilibrium, symmetric games.
    Date: 2012–06
  5. By: Gerasimou, Georgios
    Abstract: This paper proposes a model of individual choice that does not assume completeness of the decision maker's preferences. The model helps explain in a natural way, and within a unied framework of choice in the presence of preference-incomparable options, three distinct behavioural phenomena: the asymmetric dominance/attraction effect, choice deferral and status quo bias. A decision maker who follows the decision rule featured in the model chooses an alternative from a menu if it is totally preference-undominated in that menu and at the same time is also partially preference-dominant. In situations where the decision maker's preferences are complete the model delivers strict utility maximisation.
    Keywords: Attraction Effect; Choice Deferral; Status Quo Bias; Incomplete Preferences; Bounded Rationality
    JEL: D03 D11 D01
    Date: 2012–07–07
  6. By: Avner Greif; Guido Tabellini
    Abstract: Over the last millennium, the clan and the city have been the locus of cooperation in China and Europe respectively. This paper examines - analytically, historically,and empirically - the cultural, social, and institutional co-evolution that led to this bifurcation. We highlight that groups with which individuals identify are basic units of cooperation. Such groups impact institutional development because intra-group moral commitment reduces enforcement cost implying a comparative advantage in pursuing collective actions. Moral groups perpetuate due to positive feedbacks between morality, institutions, and the implied pattern of cooperation.
    Date: 2012
  7. By: Stéphane Gonzalez (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne); Michel Grabisch (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)
    Abstract: In cooperative games, the core is one of the most popular solution concept since it ensures coalitional rationality. For non-balanced games however, the core is empty, and other solution concepts have to be found. We propose the use of general solutions, that is, to distribute the total worth of the game among groups rather than among individuals. In particular, the k-additive core proposed by Grabisch and Miranda is a general solution preserving coalitional rationality which distributes among coalitions of size at most k, and is never ampty for k ≥ 2. The extended core of Bejan and Gomez can also be viewed as a general solution, since it implies to give an amount to the grand coalition. The k-additive core being an unbounded set and therefore difficult to use in practice, we propose a subset of it called the minimal bargaining set. The idea is to select elements of the k-additive core minimizing the total amount given to coalitions of size greater than 1. Thus the minimum bargaining set naturally reduces to the core for balanced games. We study this set, giving properties and axiomatizations, as well as its relation to the extended core of Bejan and Gomez. We introduce also the notion of unstable coalition, and show how to find them using the minimum bargaining set. Lastly, we give a method of computing the minimum bargaining set.
    Keywords: Cooperative game, core, balancedness, general solution.
    Date: 2012–04
  8. By: Velu, Chander (University of Cambridge); Iyer, Sriya (University of Cambridge); Gair, Jonathan R. (University of Cambridge)
    Abstract: Players cooperate in experiments more than game theory would predict. In order to explain this, we introduce the 'returns-based beliefs' approach: the expected returns of a particular strategy in proportion to the total expected returns of all strategies. Using a decision analytic solution concept, Luce's (1959) probabilistic choice model, and 'hyperpriors' for ambiguity in players' cooperability, our approach explains empirical observations in classic games such as the Prisoner's Dilemma. Testing the closeness of fit of our model on Selten and Chmura (2008) data for completely mixed 2x2 games shows that with loss aversion, returns-based beliefs explain the data better than other equilibrium concepts.
    Keywords: subjective probabilities, decision making, cooperation
    JEL: D01 D03
    Date: 2012–07
  9. By: Jonathan K. Yoder; Adrienne M. Ohler; Hayley H. Chouinard (School of Economic Sciences, Washington State University)
    Abstract: A lottery that provides participants the opportunity to choose among a set of simple gambles over multi-attribute goods results in an endogenous distribution of win rates over gambles that reflects tradeoffs between the relative desirability of the available goods and the probability of winning. These win rates provide sufficient information to estimate hedonic prices, marginal utility, and marginal rates of substitution among attributes. We develop a model for mapping preferences from this information set and apply it to Idaho’s Four Rivers Whitewater Recreation Lottery. This lottery structure shows promise as a foundation for economic experiments for preference revelation.
    Keywords: lotteries, complex goods, hedonic pricing, choice under uncertainty
    JEL: D01 D49 D84 H42 Q26
    Date: 2012
  10. By: Kvaløy, Ola (UiS); Schöttner, Anja (University of Bonn)
    Abstract: We present a model in which a motivator can take costly actions - or what we call motivational effort - in order to reduce the effort costs of a worker, and analyze the optimal combination of motivational effort and monetary incentives. We distinguish two cases. First, the firm owner chooses the intensity of motivation and bears the motivational costs. Second, another agent of the firm chooses the motivational actions and incurs the associated costs. In the latter case, the firm must not only incentivize the worker to work hard, but also the motivator to motivate the worker. We characterize and discuss the conditions under which monetary incentives and motivational effort are substitutes or complements, and show that motivational effort may exceed the efficient level.
    Keywords: Incentives; Motivate
    JEL: A10
    Date: 2012–07–17
  11. By: Jorge M. Streb; Gustavo Torrens
    Abstract: Under asymmetric information, dishonest sellers lead to market unraveling in the lemons model. An additional cost of dishonesty is that language becomes cheap talk. We develop instead a model where people derive utility from actions (what they say), as well as from outcomes, so talk is costly. We find that the existence of honest agents that mean what they say is not enough to make trade more likely, unless a traceability condition that prevents arbitrage is met. When we introduce a continuum of misrepresentation cost types and qualities, full market unraveling is not possible and babbling equilibria are eliminated. More generally, costly talk is a special kind of signal, a symbolic signal that presupposes linguistic conventions, otherwise truth and falsehood, as well as misrepresentation costs, are undefined.
    Keywords: asymmetric information, honesty, trust, symbols, signals, costly talk
    JEL: D8 C7
    Date: 2012–07
  12. By: Jun Xiao
    Abstract: This paper studies a complete-information bargaining game with one buyer and multiple sellers of di¤erent ?sizes? or bargaining strengths. The bargaining order is determined by the buyer. If the buyer can commit to a bargaining order, there is a unique subgame perfect equilibrium outcome where the buyer bargains in order of increasing size ? from the smallest to the largest. If the buyer cannot commit to a bargaining order and the sellers are su¢ ciently di¤erent, there is also a unique subgame perfect equilibrium outcome again with the order of increasing size.
    Keywords: multi-person bargaining, bargaining order
    JEL: C78
    Date: 2012
  13. By: James Bland, Simon Loertscher
    Abstract: We consider the canonical directed search framework in which sellers play pure strategies and assume that buyers play strategies that are monotone in prices, can remain inactive and choose to do so whenever their payoff from participating is zero regardless of what the other buyers do. We show that directed search equilibria, which have been the focus of the literature, are the only equilibria that satisfy these assumptions. Directed search equilibria are selected here not because buyers cannot coordinate – no such assumption is made – but because they fail to play strategies that require them to increase the demand for a seller’s good as this good becomes more expensive.
    Keywords: Directed search, monotone strategies, directed search equilibrium.
    JEL: C72 D72
    Date: 2012
  14. By: Jun Xiao
    Abstract: This paper studies complete-information, all-pay contests with asymmetric players competing for multiple heterogeneous prizes. In these contests, each player chooses a performance level or score. The first prize is awarded to the player with the highest score,the second,less valuable prize to the player with the second highest score, etc. Players are asymmetric in that they incur di¤erent costs of score. The players are assumed to have ordered marginal costs, and the prize sequence is assumed to be either quadratic or geometric. I show that each such contest has a unique Nash equilibrium and exhibit an algorithm that constructs the equilibrium. I then apply the main result to study: (a) the issue of tracking students in schools, (b) the incentive e¤ects of superstars,and (c)the optimality of winner-take-all contests.
    Keywords: all-pay, contest, asymmetric, heterogeneous
    Date: 2012
  15. By: Peter Bardsley
    Abstract: In a linear contracting environment the Fenchel transform provides a complete duality between the contract and the information rent. Through an appropriate generalised convexity this can be extended to provide a complete duality in the supermodular quasilinear contracting environment that covers the majority of applications. Using this framework, we provide a complete characterization of the allocation correspondences that can be implemented by a principal in this environment. We also address the question of when an allocation can be implemented by a menu of simple contracts. Along the way, a supermodular envelope theorem is proved, somewhat different in nature to the Milgrom Segal result.
    Keywords: mechanism design; contract theory; duality; Fenchel transform; abstract convexity
    JEL: D82 D86
    Date: 2012
  16. By: Dai, Darong
    Abstract: In the paper, we re-investigate the long run behavior of an adaptive learning process driven by the stochastic replicator dynamics developed by Fudenberg and Harris (1992). It is demonstrated that the Nash equilibrium will be the robust limit of the adaptive learning process as long as it is reachable for the learning dynamics in almost surely finite time. Doob’s martingale theory and Girsanov Theorem play very important roles in confirming the required assertion.
    Keywords: Stochastic replicator dynamics; Adaptive learning; Nash equilibria; Global convergence; Robustness
    JEL: C72 C73
    Date: 2012–05–03

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