Spatial social networks

We introduce a spatial cost topology in the network formation model analyzed by Jackson and Wolinsky, Journal of Economic Theory (1996), 71: 44–74. This cost topology might represent geographical, social, or individual differences. It describes variable costs of establishing social network connections. Participants form links based on a cost-benefit analysis. We examine the pairwise stable networks within this spatial environment. Incentives vary enough to show a rich pattern of emerging behavior. We also investigate the subgame perfect implementation of pairwise stable and efficient networks. We construct a multistage extensive form game that describes the formation of links in our spatial environment. Finally, we identify the conditions under which the subgame perfect Nash equilibria of these network formation games are stable. We are very grateful for the constructive comments of Matt Jackson and an anonymous referee. We also like to thank Vince Crawford, Marco Slikker, Edward Droste, Hans Haller, Dimitrios Diamantaras, and Sudipta Sarangi for comments on previous drafts of this paper.We acknowledge Jay Hogan for his programming support. Part of this research was done while visiting the CentER for Economic Research, Tilburg University, Tilburg, The Netherlands.Financial support from the Netherlands Organization for Scientific Resrarch (NWO), grant B46-390, is gratefully acknowledged.-->,     

Optimal design of trade institutions

We model an economy with social institutions that facilitate trade and induce three types of costs: establishment costs, access costs, and use costs. Use costs are specific transaction costs related to the use of these trade institutions. We assume that a trade institution is economically completely determined by the costs it imposes and by the effects on the trades it facilitates. We extend the Pareto efficiency concept to include various modes of organization of social institutions: the costs and benefits of these organizations are expressed in the trades they facilitate.Within this setting we discuss a valuation equilibrium concept, in which all agents use a common conjectural price system that assigns to every trade institution the price vector that would prevail under it. This feature of the equilibrium is important in securing the second welfare theorem, and is new to the analysis of economies with costly trade. Since the use costs can be nonlinear, there are non-convexities that prevent the second welfare theorem from obtaining in a finite economy, but we show it for large economies.Received: 3 April 2002, Accepted: 30 April 2003, JEL Classification: D59, D70, H49Robert P. Gilles: donewhile visiting the Center for Economic Research, Tilburg University, Tilburg, The Netherlands. Financial support from the Netherlands Organization for Scientific Research (NWO), grant B46-390, is gratefully acknowledged.Dimitrios Diamantaras: Part of this research wasSupport from Temple University via a Fuller research fellowship is gratefully acknowledged.The authors would like to thank Suzanne Scotchmer, Andreu Mas-Colell, Marcus Berliant, Shlomo Weber, Hans Haller, Dhanajay Gokhale, Julian Manning, and two anonymous referees for their valuable comments and discussions of previous drafts of this paper. A previous version of this paper was circulated as Equilibria of economies with costly trade.     

Strategy-proof allocation of fixed costs

An economy can produce and consume a fixed-cost excludable public good only if its members fully fund the cost of the good. In this paper, we characterize the entire class of mechanisms for the provision of the public good and its cost that are Pareto optimal among the set of strategy-proof, voluntarily-participatory, budget-balancing, non-bossy, and replacement-monotonic mechanisms. We demonstrate that this class of mechanisms is quite small and can be characterized as simple step-price mechanisms.Received: 10 July 2001, Accepted: 5 February 2003, JEL Classification: C72, D71This work was done while Dearden was visiting Center for Economic Research, Tilburg University, The Netherlands. He is thankful for their gracious hospitality. The authors thank the editors and reviewers for their thoughtful comments.     

Good neighbors are hard to find: computational complexity of network formation

We investigate the computational complexity of several decision problems in a simple strategic game of network formation. We find that deciding if a player has a strategy that guarantees him a certain payoff against a given strategy profile of the other players is an NP-complete problem. Deciding if there exists a strategy profile that guarantees a certain aggregate payoff is also NP-complete. Deciding if there is a Nash equilibrium in pure strategies which guarantees a certain payoff to each player is NP-hard. The problem of deciding if a given strategy profile is a Nash equilibrium is investigated as well. We would like to thank both referees for valuable corrections and suggestions and one referee in particular for a very detailed and beneficial critique. We thank Colin de la Higuera for fruitful discussions. Support by the French Ministry for Youth, Education and Research, through project SCSHS-2004-04 is gratefully acknowledged.     

Coordinating under incomplete information

We show that, in a minimum effort game with incomplete information where player types are independently drawn, there is a largest and smallest Bayesian equilibrium, leading to the set of equilibrium payoffs (as evaluated at the interim stage) having a lattice structure. Furthermore, the range of equilibrium payoffs converges to those of the deterministic complete information version of the game, in the limit as the incomplete information vanishes. This entails that such incomplete information alone cannot explain the equilibrium selection suggested by experimental evidence. We thank Atila Abdulkadiroglu, Hans Carlsson, Ani Guerdjikova and an anonymous referee for helpful comments. Part of this work was done while Asheim was visiting Cornell University, which hospitality is gratefully acknowledged.     

Change point tests based on U-statistics with applications in reliability

We consider the problem of testing the null hypothesis of no change against the alternative of exactly one change point. The proposed tests are based on generalized two-sample U-statistic processes. We drive the limiting null distributions of the proposed tests. Some applications in Statistical Reliability are given. This research was supported by an NSERC Canada grant at the University of Alberta. Part of this research was done while visiting the University of Alberta supported by the NSERC Canada grant of the first author.     

Implementing efficient market structure

Abstract. This article studies the design of optimal mechanisms to regulate entry in natural oligopoly markets, assuming the regulator is unable to control the behavior of firms once they are in the market. We adapt the Clarke–Groves mechanism, characterize the optimal mechanism that maximizes the weighted sum of expected social surplus and expected tax revenue, and show that these mechanisms avoid budget deficits and prevent excessive entry. Received: 7 May 2001 / Accepted: 24 June 2002 We would like to thank seminar participants at Bonn and Berlin, in particular Peter Bank, Wieland Müller, and Urs Schweizer, the two anonymous referees, and the associate editor for most useful and exceptionally detailed comments. Financial support was received by the Deutsche Forschungsgemeinschaft, SFB 373 (“Quantifikation und Simulation ?konomischer Prozesse”), Humboldt–Universit?t zu Berlin.     

Corporate governance and pay for performance: evidence from Germany

This paper investigates how two distinctive features of the German corporate governance system—concentrated ownership structure and representation of employees on firm supervisory boards—influence the sensitivity of managerial pay to firm profitability. There is a positive, though very small, link between pay and profitability for widely held firms. The presence of a largest owner seems hardly to affect this link in any economically significant way. However, the link between pay and profitability is smaller and indeed not significantly different from zero in firms whose largest owner is a German financial institution. This suggests that large owners tend to act as a substitute for rather than a complement to performance related pay in Germany. We thank Dennis Leech for allowing us to use his algorithms for computing voting power indices, and Brian Cheffins, Tim Guinnane, Andrew Harvey, Dennis Leech, Hamish Low, Sheilagh Ogilvie, Melvyn Weeks and two anonymous referees for helpful comments. The research reported in this paper was started during a joint visit to CES, University of Munich, and completed during visits of Edwards and Weichenrieder to the University of Konstanz and the ifo Institute for Economic Research in Munich. We thank the three institutions for their hospitality, especially Bernd Genser and Hans-Werner Sinn. A previous version of this paper was circulated under the title “The Measurement of Firm Ownership and its Effect on Managerial Pay”.     

Explaining Income Nonresponse – A Case Study by means of the British Household Panel Study (BHPS)

Many validation studies deal with item nonresponse and measurement error in earning data. In this paper, we explore motives of respondents for the failure to reveal earnings using the British Household Panel Study (BHPS). The BHPS collects socio-economic information of private households in Great Britain. We explain the evolution of income-nonresponse in the BHPS and demonstrate the importance of a discrimination between refusing the income-statement or don’t know. This study is done during my fellowship at the University Essex and is part of the ECASS Project “Respondent Behaviour in Panel Studies”. In particular I would like to thank Heather Laurie, Cheti Nicoletti and Peter Lynn (ISER, Essex) as well as Gert G. Wagner (DIW Berlin and Berlin University of Technology, TUB) for helpful comments. The usual disclaimer applies.     

The generalized Stackelberg equilibrium of the all-pay auction with complete information

We characterize the equilibrium of the all-pay auction with general convex cost of effort and sequential effort choices. We consider a set of n players who are arbitrarily partitioned into a group of players who choose their efforts ‘early’ and a group of players who choose ‘late’. Only the player with the lowest cost of effort has a positive payoff in any equilibrium. This payoff depends on his own timing vis-a-vis the timing of others. We also show that the choice of timing can be endogenized, in which case the strongest player typically chooses ‘late’, whereas all other players are indifferent with respect to their choice of timing. In the most prominent equilibrium the player with the lowest cost of effort wins the auction at zero aggregate cost. We thank Dan Kovenock and Luis C. Corchón for discussion and helpful comments. The usual caveat applies. Wolfgang Leininger likes to express his gratitude to Wissenschaftszentrum Berlin (WZB) for its generous hospitality and financial support.     

Stable and efficient bargaining networks

Abstract. We examine a bargaining game among players connected by a network, where successively potential partners negotiate over terms of a project. For any network structure and ordering of selection of bargaining partners, there is a unique subgame perfect equilibrium outcome which coincides with the standard Rubinstein split. Based on this, we derive expected payoffs for players as a function of the network. We the characterize the pairwise stable and efficient bargaining networks. These two sets do not always coincide and in many situations pairwise stable networks are over-connected. Received: 10 April 2001 / Accepted: 17 January 2002 I am indebted to Matthew Jackson for suggesting this paper. I also thank Bernard Caillaud, Sanjeev Goyal, and the seminar participants at Universidad de Alicante, Universidad Carlos III de Madrid, CEMFI (Madrid), Universitat Autònoma de Barcelona, Erasmus University of Rotterdam, Universitat Pompeu Fabra (Barcelona) and CERAS (Paris) for helpful comments. This paper was written while at Universitat Pompeu Fabra and CERAS. Financial support from the Spanish Ministry of Education through research grant DGESIC PB96-0302, and from the Ecole Nationale des Ponts et Chaussées, Paris is gratefully acknowledged. All errors are of course mine.     

Is there a Political Support for the Double Burden on Prolonged Activity?

In many countries elderly workers are subject to a double distortion when they consider prolonging their activity: the payroll tax and a reduction in their pension rights. It is often argued that such a double burden would not be socially desirable. We consider a setting where it would be rejected by both a utilitarian and a Rawlsian social planner. Furthermore, each individual would also reject it as a citizen candidate. We show that the double burden may nevertheless be (second-best) Pareto efficient and can be supported by a particular structure of social weights biased towards the more productive workers. The paper has been presented at the “Atelier Retraites”, Bordeaux, October 2003. We would like to thank the participants and in particular our discussant, Ronan Mahieu, for their remarks. We are also grateful to our two referees who provided detailed and constructive comments and suggestions. Support for this research project has been provided by the European RTN program through the FINRET network     

Bayesian Nash equilibrium and variational inequalities

This paper provides a sufficient condition for the existence and uniqueness of a Bayesian Nash equilibrium by regarding it as a solution of a variational inequality. The payoff gradient of a game is defined as a vector whose component is a partial derivative of each player’s payoff function with respect to the player’s own action. If the Jacobian matrix of the payoff gradient is negative definite for each state, then a Bayesian Nash equilibrium is unique. This result unifies and generalizes the uniqueness of an equilibrium in a complete information game by Rosen (1965) and that in a team by Radner (1962). In a Bayesian game played on a network, the Jacobian matrix of the payoff gradient coincides with the weighted adjacency matrix of the underlying graph.     

Non-self-averaging of a two-person game with only positive spillover: a new formulation of Avatamsaka’s dilemma

In this game [Aruka in Avatamsaka game structure and experiment on the web. In: Aruka Y (ed) Evolutionary controversies in economics. Springer, Tokyo, pp 115–132, 2001], selfishness may not be determined even if an agent selfishly adopts the strategy of defection. Individual selfishness can only be realized if the other agent cooperates, therefore gain from defection can never be assured by defection alone. The sanction by defection as a reaction of the rival agent cannot necessarily reduce the selfishness of the rival. In this game, explicit direct reciprocity cannot be guaranteed. Now we introduce different spillovers or payoff matrices, so that each agent may then be faced with a different payoff matrix. A ball in the urn is interpreted as the number of cooperators, and the urn as a payoff matrix. We apply Ewens’ sampling formula to our urn process in this game theoretic environment. In this case, there is a similar result as in the classic case, because there is “self-averaging” for the variances of the number who cooperate. Applying Pitman’s sampling formula to the urn process, the invariance of the random partition vectors under the properties of exchangeability and size-biased permutation does not hold in general. Pitman’s sampling formula depends on the two-parameter Poisson–Dirichlet distribution whose special case is just Ewens’ formula. In the Ewens setting, only one probability α of a new entry matters. On the other hand, there is an additional probability θ of an unknown entry, as will be argued in the Pitman formula. More concretely, we will investigate the effects of different payoff sizes from playing a series of different games for newly emerging agents. As Aoki and Yoshikawa (Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics, Economics Discussion Papers 2007-49. . November 26, 2007) and Aoki (J Econ Interact Coord 3:1–3, 2008) dealt with a product innovation and a process innovation, they criticized Lucas’ representative method and the idea that players face micro shocks drawn from the same unchanged probability distribution. In the light of Aoki and Yoshikawa (Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics, Economics Discussion Papers 2007-49. . November 26, 2007), we show the same argument in our Avatamsaka game with different payoffs. In this setting, innovations occurring in urns may be regarded as increases of the number of cooperators in urns whose payoffs are different.     

Elections and strategic positioning games

We formalize the interplay between expected voting behavior and strategic positioning behavior of candidates as a common agency problem in which the candidates (i.e., the principals) compete for voters (i.e., agents) via the issues they choose and the positions they take. A political situation is defined as a feasible combination of candidate positions and expected political payoffs to the candidates. Taking this approach, we are led naturally to a particular formalization of the candidates' positioning game, called a political situation game. Within the context of this game, we define the notion of farsighted stability (introduced in an abstract setting by Chwe 1994) and apply Chwe's result to obtain existence of farsightedly stable outcomes. We compute the farsightedly stable sets for several examples of political situations games, with outcomes that conform to real-world observations.Received: 18 May 2001, Accepted: 22 January 2002, JEL Classification: C7, D7, D8Myrna H. Wooders: http://www.warwick.ac.uk/fac/soc/Economics/wooders/An earlier version of this paper was completed while the first author was visiting the Department of Economics, University of Exeter. The first author gratefully acknowledges Exeter's support and hospitality. Similarly, the second author gratefully acknowledges the support and hospitality of the Centre for Operations Research and Econometrics (CORE) of the University of Louvain-la-Neuve, Belgium and of the University of Cergy-Pontoise, France. Both authors are indebted to Amrita Dhillon, John Duggan and Gilat Levy for helpful comments about references. Both authors thank an anonymous referee for helpful comments.     

Link bidding in laboratory networks

This paper presents the results of laboratory experiments that explore the network formation process. Performances of three institutions, each derived from theoretical models found in the literature, are compared. All three institutions are found to generate similar levels of efficiency. In hospitable environments, the institutions achieve 85% efficiency, but all three fail to generate any positive surplus when stress tested.Received: 28 May 2002, Accepted: 14 March 2003, JEL Classification: A14, C70, C90, D20The authors wish to thank the International Foundation for Research in Experimental Economics for financial support in the form of subject payment money. This work has greatly benefited from comments by an anonymous referee, Rob Gilles, participants in the Social Network session at the 2001 Southern Economic Association Meetings, and seminar participants at the University of Arkansas.     

On testing for independence against right tail increasing in bivariate models

A random variableY is right tail increasing (RTI) inX if the failure rate of the conditional distribution ofX givenY>y is uniformly smaller than that of the marginal distribution ofX for everyy0. This concept of positive dependence is not symmetric inX andY and is stronger than the notion of positive quadrant dependence. In this paper we consider the problem of testing for independence against the alternative thatY is RTI inX. We propose two distribution-free tests and obtain their limiting null distributions. The proposed tests are compared to Kendall's and Spearman's tests in terms of Pitman asymptotic relative efficiency. We have also conducted a Monte Carlo study to compare the powers of these tests.Research supported by an NSERC Canada operating grant at the University of Alberta.Part of this research was done while visiting the University of Alberta supported by the NSERC Canada grant of the first author.     

Deterministic multi-player Dynkin games

A multi-player Dynkin game is a sequential game in which at every stage one of the players is chosen, and that player can decide whether to continue the game or to stop it, in which case all players receive some terminal payoff.We study a variant of this model, where the order by which players are chosen is deterministic, and the probability that the game terminates once the chosen player decides to stop may be strictly less than 1.We prove that a subgame-perfect ε-equilibrium in Markovian strategies exists. If the game is not degenerate this ε-equilibrium is actually in pure strategies.     

Endogenous coalition formation in contests

This paper analyzes coalition formation in a model of contests with linear costs. Agents first form groups and then compete by investing resources. Coalitions fight for a prize that is assumed to be subject to rivalry, so its value is non-increasing in the size of the group that obtains it. This formulation encompasses as particular cases some models proposed in the rent-seeking literature. We show that the formation of groups generates positive spillovers and analyze two classes of games of coalition formation. A contest among individual agents is the only stable outcome when individual defections leave the rest of the group intact. More concentrated coalition structures, including the grand coalition, are stable when groups collapse after a defection, provided that rivalry is not too strong. Results in a sequential game of coalition formation suggest that there exists a non-monotonic relationship between the level of underlying rivalry and the level of social conflict.

“If men were supplied with every thing in the same abundance, justice and injustice would be equally unknown among mankind.” David Hume (1740), A Treatise of Human Nature

I thank Luis Corchón, Joan Esteban, Michelle Garfinkel and József Sákovics for their comments and suggestions on the paper.     

Rationalizability in continuous games

Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff function of each player is bounded and continuous. We prove that in this class of games the process of sequentially eliminating “never-best-reply” strategies terminates before or at the first uncountable ordinal, and this bound is tight. Also, we examine the connection between this process and common belief of rationality in the universal type space of Mertens and Zamir (1985).