The consensus value: a new solution concept for cooperative games

To generalize the standard solution for 2-person TU games into n-person cases, this paper introduces a recursive two-sided negotiation process to establish cooperation between all players. This leads to a new solution concept for cooperative games: the consensus value. An explicit comparison with the Shapley value is provided, also at the axiomatic level. Moreover, a class of possible generalizations of the consensus value is introduced and axiomatized with the Shapley value at one end and the equal surplus solution at the other. Finally, we discuss a non-cooperative mechanism which implements the consensus value.     

A value for games with coalition structures

This paper presents an axiomatization of a value for games with coalition structures which is an alternative to the Owen Value. The motor of this new axiomatization is a consistency axiom based on an associated game, which is not a reduced game. The new value of an n-player unanimity game is the compound average of the new values of all the (n-1)-player unanimity games. The new value of a unanimity game allocates to bigger coalitions a larger share of the total wealth. Note that the Owen value allocates to all the coalitions the same share independently of their size.     

The role and function of drinking games in a university community

Understanding the role of drinking games in college student life is critical for program planners who wish to develop education and prevention programs to reduce abusive drinking. Drinking games are popular social activities that provide a focus for social interactions but place students at considerable risk for serious consequences. This article reports preliminary results of a study using participant observation and in-depth interviews to develop a typology of drinking games and describe patterns and practices associated with the games.     

The lottery player in Cameroon: An exploratory study

We report on an ongoing survey of attitudes toward gambling in the two main cities of Cameroon, Douala and Yaounde. From the data it appears that lottery playing in Cameroon is an answer to the economic crisis that has plagued the country for some years. The results are similar to the ones obtained in previous Canadian, American and other studies in various countries.We thank Alain Njoh Soppo and Martin Tiako, students at the business school of the University of Douala (ESSEC) who collected the data for their Mémoire de fin d'études. We also thank our research assistant, Alain Tremblay, for his help and CIDA, ESSEC and Loto-Québec for their financial help. All remaining errors are solely our own.     

The possibility of efficient provision of a public good in voluntary participation games

In this study, we provide the conditions for efficient provision of a public good in a participation game in which a non-negative integer number of units of the public good can be provided. In the case in which at most one unit of the public good can be provided, we provide refinements of Nash equilibria at which agents choose only a Nash equilibrium with an efficient allocation and provide sufficient conditions for cost-sharing rules that guarantee the existence of a Nash equilibrium with an efficient allocation. In the case of a multi-unit public good, we provide a necessary and sufficient condition for the existence of a Nash equilibrium with an efficient allocation and prove that Nash equilibria are less likely to support efficient allocations if the participation of many agents is needed for efficient provision of the public good in the case of identical agents. I would like to thank Koichi Tadenuma, Yukihiro Nishimura, Toshiyuki Fujita, John Weymark, Tatsuyoshi Saijo, Takehiko Yamato, Toshiji Miyakawa, Motohiro Sato, Takashi Shimizu, Nobue Suzuki, and Dirk T. G. Rübbelke for helpful comments and suggestions. I also thank the anonymous referees for detailed comments and suggestions. This research was supported by the Japanese Economic Research Foundation and the Grand-in-Aid for Young Scientists (Start-up) from the Japan Society for the Promotion of Science. Any remaining errors are my own.     

The role of morals in three-player ultimatum games

We experimentally investigate the role of moral concerns in three-player ultimatum bargaining. In our experimental paradigm, proposers can increase the overall size of the pie at the expenses of an NGO that conducts humanitarian aid in emergency areas. In a first study, we find that responders are not willing to engage in ‘immoral’ transactions only when fully informed about proposers’ behavior toward the NGO. Under complete information, their willingness to reject offers increases with the strength of the harm to the NGO. Moreover, the possibility to compensate the NGO through rejection further increases their willingness to reject. In a second study aimed at gauging the importance of different motives behind rejections, we show that the two most prevalent motives are to compensate the NGO or to diminish inequality between responders and proposers. Punishing proposers’ unkind intentions towards the NGO or rejecting on the basis of pure deontological reasons constitute less important motives.     

The power of a collectivity to act in weighted voting games with many small voters

We analyze the propensity to approve a random proposal of a large committee that makes decisions by weighted voting. The approach is a generalized version of James Coleman’s “power of a collectivity to act”. Throughout the paper it is assumed that the voters are of two kinds: a fixed (possibly empty) set of “major” (big) voters with fixed weights, and an ever-increasing number of “minor” (small) voters, whose total weight is also fixed, but where each individual’s weight becomes negligible. As our main result, we obtain that asymptotically many minor voters act like a modification of the quota for the vote among major voters. The paper estimates the rate of convergence which turns out to be very high if the weight distribution among the small voters is not too skewed. The results obtained are illustrated by evaluating the decision rules for the Council of Ministers of the EU for various scenarios of EU enlargement. I wish to thank Matthew Braham, Sidartha Gordon, Maurice Koster, Moshé Machover, Guillermo Owen and two anonymous referees for helpful comments.     

The geometry of implementation: a necessary and sufficient condition for straightforward games

 We characterize games which induce truthful revelation of the players’ preferences, either as dominant strategies (straightforward games) or in Nash equilibria. Strategies are statements of individual preferences on R ⁿ . Outcomes are social preferences. Preferences over outcomes are defined by a distance from a bliss point. We prove that g is straightforward if and only if g is locally constant or dictatorial (LCD), i.e., coordinate-wise either a constant or a projection map locally for almost all strategy profiles. We also establish that: (i) If a game is straightforward and respects unanimity, then the map g must be continuous, (ii) Straightforwardness is a nowhere dense property, (iii) There exist differentiable straightforward games which are non-dictatorial. (iv) If a social choice rule is Nash implementable, then it is straightforward and locally constant or dictatorial. Received: 30 December 1994/Accepted: 22 April 1996     

The Nakamura numbers for computable simple games

The Nakamura number of a simple game plays a critical role in preference aggregation (or multi-criterion ranking): the number of alternatives that the players can always deal with rationally is less than this number. We comprehensively study the restrictions that various properties for a simple game impose on its Nakamura number. We find that a computable game has a finite Nakamura number greater than three only if it is proper, nonstrong, and nonweak, regardless of whether it is monotonic or whether it has a finite carrier. The lack of strongness often results in alternatives that cannot be strictly ranked. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users. We would like to thank an anonymous referee for useful suggestions. The discussion in footnote 3 and Remark 4, among other things, would not have been possible without his/her suggestion.     

Measuring influence in command games

In the paper, we study a relation between command games proposed by Hu and Shapley and an influence model. We show that our framework of influence is more general than the framework of the command games. We define several influence functions which capture the command structure. These functions are compatible with the command games, in the sense that each commandable player for a coalition in the command game is a follower of the coalition under the command influence function. Some of the presented influence functions are equivalent to the command games, that is, they are compatible with the command games, and additionally each follower of a coalition under the command influence function is also a commandable player for that coalition in the command games. For some influence functions we define the equivalent command games. We show that not for all influence functions the compatible command games exist. Moreover, we propose a more general definition of the influence index and show that under some assumptions, some power indices, which can be used in the command games, coincide with some expressions of the weighted influence indices. Both the Shapley–Shubik index and the Banzhaf index are equal to a difference between the weighted influence indices under some influence functions, and the only difference between these two power indices lies in the weights for the influence indices. An example of the Confucian model of society is broadly examined. The authors wish to gratefully thank two anonymous referees for useful suggestions concerning this paper.     

Farsighted stability in hedonic games

We investigate how rational individuals partition themselves into different coalitions in hedonic games (see Banerjee et al. 2001 and Bogomolnaia and Jackson 2002), where individuals' preferences depend solely on the composition of the coalition they belong to. Given that the four solution concepts studied in the literature (core, Nash stability, individual stability and contractual individual stability) may exhibit myopia on the part of the players, we amend these notions by endowing players with foresight in that they look many steps ahead and consider only credible outcomes. We study the properties of the farsighted stability solutions; in particular, we show that when preferences are strict, coalition structures in the core are farsighted stable and a similar result also holds for Nash stability but not for individual stability and contractual individual stability. We thank Birgit Grodal, Hideo Konishi, an associate editor and two referees for their helpful comments and suggestions. Thanks also go to the audiences at University of Copenhagen, CSAET, 2001, Workshop on Coalitions and Networks at Warwick, 2001, and International Game Theory Conference at Stony Brook, 2001.     

The regeneration games: purity and security in the Olympic city

This paper examines the wider social impacts of hosting the London 2012 Olympic Games and its 'legacy' ambitions in East London, emphasizing securitization as an inbuilt feature of the urban regeneration project. Drawing on extensive original empirical research, the paper analyses the modalities of Olympic safety and security practices within the Olympic Park itself and their wider impact, while also connecting this research to theorization and debates in urban sociology and criminology. In this complex setting, a raft of formal and informal, often subtle, regulatory mechanisms have emerged, especially as visions of social ordering focused on 'cleansing' and 'purifying' have 'leaked out' from the hyper-securitized 'sterilized' environment of the Olympic Park and become embedded within the Olympic neighbourhood. In such complex circumstances, applying Douglas' (1966) work on purity and danger to the spatial realm provides a key conceptual framework to understand the form and impact of such processes. The imposition of order can be seen to not only perform 'cleansing' functions, but also articulate multiple symbolic, expressive and instrumental roles.     

Stability of voting games

This paper generalizes the result of Le Breton and Salles (1990) about stable set (far-sighted core of order 1) for voting games to far-sighted core of arbitrary order. Let m be the number of alternatives, n be the number of voters and G(n,k) be a proper symmetric simple game in which the size of a winning coalition is greater or equal to k. It is shown that the far-sighted core of order d for G(n,k) is nonempty for all preference profiles and for all n and k with n/(n–k)=v ¹ iff m(d+1)(v–1).This paper is part of my dissertation. I am grateful to my thesis advisor Leonid Hurwicz for his guidance and encouragement. I would like to thank Edward Green, Lu Hong, James Jordan, Andrew McLennan, Herve Moulin and Marcel Richter for their very helpful suggestions. Especially a referee and Maurice Salles made many good comments. Of course, any errors that remain are the sole responsibility of the author.     

The likelihood of inefficiency,a prisoner's dilemma and suboptimality in games of binary voluntary provision of public goods

This paper focuses on one possible measure for the severity of the problems of inefficiency, suboptimality and the Prisoner's Dilemma in voluntary public-good provision. The proposed measure is the probability of the emergence of the respective problem in an impartial environment where all feasible combinations of the parameters of the voluntary public good provision game are equally likely. These probabilities are derived using the game of voluntary binary contributions to the provision of public goods recently analyzed by Gradstein and Nitzan (1990). The severity of the three problems (Prisoner's Dilemma, suboptimality and inefficiency) is computed, respectively for games with up to N=12, N=6 and N=4 players. The decreasing order of N reflects the increasing complexity of the problems and, in turn, computation of their likelihood. It turns out that the likelihoods of all three problems are increasing with the number of players, N. More importantly, social optimality is more likely than suboptimality when N2, efficiency is more likely than inefficiency when N3 and no Prisoner's Dilemma is more likely than a Prisoner's Dilemma when N5.     

Depth of reasoning in strategic form games

The depth of human reasoning in interactive decision-making situations can be assessed experimentally in dominance solvable non-cooperative games. We first review the studies employing two sorts of games—the Beauty Contest game and the Investment game. Studies employing these games show that: (i) people typically engage in relatively low levels of strategic reasoning; and (ii) there are individual differences in the depth of reasoning. There are other lines of research employing other types of games and definitions of the depth of reasoning that support the two conclusions above. We argue that these studies underestimate depth of reasoning because it is also necessary to apply a mental model about other players’ reasoning ability in order to play well. Implications of those findings to the theory-of-mind or Machiavellian Intelligence research are discussed.