Axiomatizations of the normalized Banzhaf value and the Shapley value

A cooperative game with transferable utilities– or simply a TU-game – describes a situation in which players can obtain certain payoffs by cooperation. A solution concept for these games is a function which assigns to every such a game a distribution of payoffs over the players in the game. Famous solution concepts for TU-games are the Shapley value and the Banzhaf value. Both solution concepts have been axiomatized in various ways. An important difference between these two solution concepts is the fact that the Shapley value always distributes the payoff that can be obtained by the `grand coalition' consisting of all players cooperating together while the Banzhaf value does not satisfy this property, i.e., the Banzhaf value is not efficient. In this paper we consider the normalized Banzhaf value which distributes the payoff that can be obtained by the `grand coalition' proportional to the Banzhaf values of the players. This value does not satisfy certain axioms underlying the Banzhaf value. In this paper we introduce some new axioms that characterize the normalized Banzhaf value. We also provide an axiomatization of the Shapley value using similar axioms. Received: 10 April 1996 / Accepted: 2 June 1997     

The Chairman’s Paradox Revisited

This paper re-examines the so-called ‘chairman’s paradox‘ that was first noticed by Farquharson in his path breaking tract on sophisticated voting, Theory of Voting (1969). The Chairman’s paradox is concerned with the case of a three member committee in which a particular player who has a regular and a tie-breaking vote – the ‘chairman’ – not only will do worse in specific instances under the plurality procedure for three alternatives than if he did not have such a vote, but will also do worse overall. That is, the chairman’s a priori probability of success (‘getting what one wants’) for all possible games with linear (strict) preference orders is lower than that of the two regular members. It is demonstrated that this result, which comes about if voters act strategically rather than sincerely, is not as robust as it has been thought to be. By merely replacing the standard assumption of linear preference orders with weak preference orders, which allow for indifference, we can escape from the paradox for the canonical case of three players and three alternatives. With weak preference orders, the a priori success of the chairman is now greater than that of the other two players. We also point to a new paradox of sophisticated voting.     

Core concepts for share vectors

A value mapping for cooperative games with transferable utilities is a mapping that assigns to every game a set of vectors each representing a distribution of the payoffs. A value mapping is efficient if to every game it assigns a set of vectors which components all sum up to the worth that can be obtained by all players cooperating together.? An approach to efficiently allocate the worth of the ‘grand coalition’ is using share mappings which assign to every game a set of share vectors being vectors which components sum up to one. Every component of a share vector is the corresponding players' share in the total payoff that is to be distributed among the players. In this paper we discuss a class of share mappings containing the (Shapley) share-core, the Banzhaf share-core and the Large Banzhaf share-core, and provide characterizations of this class of share mappings. Received: 9 August 1999/Accepted: 25 April 2000     

TO DETER OR TO MODERATE? ALLIANCE FORMATION IN CONTESTS WITH INCOMPLETE INFORMATION

We consider two players' choice about the formation of an alliance ahead of conflict in a framework with incomplete information about the strength of the potential ally. When deciding on alliance formation, players anticipate the self‐selection of other players and the informational value of own and other players' choices. In the absence of these signaling effects, strong players have an incentive to stand alone, which leads to a separating equilibrium. This separating equilibrium can be destabilized by deception incentives if beliefs are updated on the basis of endogenous alliance formation choices. Weak players may find it attractive to appear strong in order to deter competitors from positive effort choices. Strong players may find it attractive to appear weak in order to give their competitors a false sense of security and then beat them with little effort. Moreover, appearing weak allows players to free‐ride when alliances are formed. (JEL D72, D74)     

Agenda control in coalition formation

Theoretical models of government formation in political science usually assume that the head of state is non-strategic. In this paper, we analyze the power of an agenda setter who chooses the order in which players are recognized to form coalitions in simple games. We characterize those sets of players which can be imposed in the equilibrium coalition and show that the only decisive structures where the agenda setter can impose the presence of any minimal winning coalition are apex games, where a large player forms a winning coalition with any of the small players. Keywords: Government Formation, Agenda Control, Coalitional Bargaining, Finite Bargaining Rules. Received: 26 January 2001/Accepted: 31 July 2001     

A universal meta bargaining implementation of the Nash solution

This paper follows van Damme (1986) in presenting a meta bargaining approach that justifies the Nash bargaining solution. But in contrast to van Damme's procedure our meta bargaining game is universal in the sense that all bargaining solutions are allowed as strategic choices in the meta bargaining game. Also our result holds true for any number n of players. Received: 31 July 2000/Accepted: 19 March 2001     

PRIZE SCARCITY AND OVERDISSIPATION IN ALL‐PAY AUCTIONS

We compare bidding behavior in complete information all‐pay auction experiments that vary in the prizes and number of players. We confirm the observation from prior single‐prize experiments that there is overbidding relative to equilibrium predictions. Our primary results are that increasing the number of prizes and players proportionally does not reduce overbidding but increasing the number of prizes with a fixed number of players eliminates overbidding. We conclude that the overbidding phenomenon is related to the scarcity of the prize. We provide new theoretical results on the multi‐prize logit equilibrium, and our experimental results are qualitatively consistent with logit equilibrium predictions. (JEL D72, D91, C91, D44)     

THREE‐PLAYER TRUST GAME WITH INSIDER COMMUNICATION

We examine behavior in a three‐player trust game in which the first player may invest in the second and the second may invest in the third. Any amount sent from one player to the next is tripled. The third player decides the final allocation among three players. The baseline treatment with no communication shows that the first and second players send significant amounts and the third player reciprocates. Allowing insider communication between the second and the third players increases cooperation between these two. Interestingly, there is an external effect of insider communication: the first player who is outside communication sends 54% more and receives 289% more than in the baseline treatment. As a result, insider communication increases efficiency from 44% to 68%. (JEL C72, C91, D72)     

Kingmakers and leaders in coalition formation

Assume that players strictly rank each other as coalition partners. We propose a procedure whereby they “fall back” on their preferences, yielding internally compatible, or coherent, majority coalition(s), which we call fallback coalitions. If there is more than one fallback coalition, the players common to them, or kingmakers, determine which fallback coalition will form. The first player(s) acceptable to all other members of a fallback coalition are the leader(s) of that coalition. The effects of different preference assumptions—particularly, different kinds of single-peakedness—on the number of coherent coalitions, their connectedness, and which players become kingmakers and leaders are investigated. The fallback procedure may be used (i) empirically to identify kingmakers and leaders or (ii) normatively to select them. We illustrate the model using data from the U.S. Supreme Court, 2005–2009.     

FAIR ALLOCATION WHEN PLAYERS' PREFERENCES ARE UNKNOWN

Suppose an arbitrator needs to allocate an asset among two players, whose claims on the asset are incompatible. The allocation outcome is said to be fair if the arbitrator awards an outcome that brings the same utility payoff to the two players whenever the two players' claims are symmetric and the allocation set is symmetric. In conjunction with other natural axioms, this fairness requirement implies a unique allocation outcome for any claims problem. We propose a mechanism which can be used by the arbitrator to implement this allocation outcome, even when the players' preferences are unknown to the arbitrator. (JEL C78, D63, J52)     

THE ATTACK‐AND‐DEFENSE GROUP CONTESTS: BEST SHOT VERSUS WEAKEST LINK

This study analyzes a group contest in which one group (defenders) follows a weakest link, whereas the other group (attackers) follows a best shot impact function (IF). We fully characterize the Nash and coalition‐proof equilibria and show that with symmetric valuation the coalition‐proof equilibrium is unique up to the permutation of the identity of the active player in the attacker group. With asymmetric valuation, it is always an equilibrium for one of the highest valuation players to be active; it may also be the case that the highest valuation players in the attacker group free‐ride completely on a group member with a lower valuation. However, in any equilibrium, only one player in the attacker group is active, whereas all the players in the defender group are active and exert the same effort. We also characterize the Nash and coalition‐proof equilibria for the case in which one group follows either a best shot or a weakest link but the other group follows an additive IF. (JEL C72, D70, D72, D74, H41)     

Assessment of Cardiovascular Risk in Collegiate Football Players and Nonathletes

Abstract

Collegiate American football players may be at risk for cardiovascular disease. Objective: To compare cardiovascular disease risk factors and cardiovascular structure and function parameters of football players, stratified by position, to a group of sedentary, nonathletes. Participants: Twenty-six collegiate football players and 13 nonathletes participated in this study. Methods: Blood pressures, anthropometrics, and blood chemistries were obtained and analyzed using standardized procedures. Resting echocardiography was used to evaluate cardiac morphology and function. Brachial artery flow-mediated dilation was assessed using high-resolution ultrasonography. Results: The prevalence of the metabolic syndrome was significantly higher amongst the linemen compared to the skill-position players (46% versus 0%, p < .05). Mildly abnormal wall thickness was noted in 20% of the football players. No significant differences in vascular function were observed between the groups. Conclusions: The increased prevalence of the metabolic syndrome and its components in the collegiate linemen may increase cardiovascular disease risk.     

BEHAVIORAL PATTERNS IN SOCIAL NETWORKS

In this article, we focus on the analysis of individual decision‐making for the formation of social networks, using experimentally generated data. We analyze the determinants of the individual demand for links under the assumption of agents' static expectations and identify patterns of behavior that correspond to three specific objectives: players propose links so as to maximize expected profits (myopic best response strategy); players attempt to establish the largest number of direct links (reciprocator strategy); and players maximize expected profits per direct link (opportunistic strategy). These strategies explain approximately 74% of the observed choices. We demonstrate that they are deliberately adopted and, by means of a finite mixture model, well identified and separated in our sample. (JEL C33, C35, C90, D85)     

Psychosocial experiences of concussed collegiate athletes: The role of emotional support in the recovery process

Abstract

Objective: Understand from whom concussed football players seek and receive emotional support, and whether this support is associated with injury perceptions. Participants: Football players (N?=?26) from three NCAA Division I programs. Methods: With approval from the head athletic trainer, concussed athletes (2017 season) completed short surveys within 4–6?days of diagnosis and when cleared to return. Results: Concussed athletes perceived their injury as a normal consequence of playing football, not serious, and reported little, if any, depression and anxiety. Athletes reported the most support from athletic trainers; the least from coaches and teammates. Emotional support was associated with fewer adverse psychosocial reactions, more sport-injury related growth, and greater intentions to report future concussion symptoms. Conclusion: Results from this pilot study suggest that emotional support during the concussion recovery process should be understood and fostered by university officials charged with the health and well-being of collegiate football players.     

SOCIAL HIERARCHIES: A LABORATORY STUDY ON PUNISHMENT PATTERNS ACROSS NETWORKS

We experimentally study punishment patterns across network structures, and their effect on cooperation. In a repeated public goods setting, subjects can only observe and punish their neighbors. Centralized structures (like the star network) outperform other incomplete networks and reach contribution levels like the ones observed in a complete network. Our results suggest that hierarchical network structures with a commonly observed player benefit more from sanctions not because central players punish more, but because they follow, and promote, different punishment patterns. While quasi-central players in other incomplete architectures (like the line network) retaliate, and get trapped in the vicious circle of antisocial punishment, central players in the star network do not punish back, increase their contributions when sanctioned by peripheral players, and sanction other participants in a prosocial manner. Our results illustrate recent field studies on the evolutionary prevalence of hierarchical networks. We document a network-based rationale for this positive effect in an identity-free, fully anonymous environment. (JEL C72, C91, C92, D90, H41)     

Personality and psychographics of three types of gamblers in the United States

Using the results of the Experian Marketing Services' Simmons^® National Consumer Study (NCS) (N₀ = 24,581), this paper studies the characteristics of three types of US. gamblers: regular lottery players (N₁ = 1100), heavy casino gamblers (N₂ = 636) and online gamblers (N₃ = 291). We explore each type of gambler using measures of several personality and psychographic variables: impulsiveness, desire for control, materialism, risk taking, self-centredness, introversion, sensation seeking and financial prudence. We find that while all three groups have elevated levels of impulsiveness and materialism relative to non-gamblers (p < 0.01), most noteworthy are the online gamblers, who have higher levels of risk taking, desire for control, self-centredness and sensation seeking compared to casino gamblers, lottery players and non-gamblers (p < 0.01). This study additionally emphasizes the importance of considering demographics when investigating psychographics, as some of the psychographics related to gambling are conditioned on age. In addition, we find that online gamblers who also engage in other forms of gambling may be distinct from those who do not, suggesting they are not a homogeneous group.     

AN EXPERIMENTAL STUDY OF KIN AND ETHNIC FAVORITISM

Ethnic and kinship ties have long been viewed as potential catalysts for favoritism, and hence corruption. In experiments conducted in three countries, we recruit siblings, coethnics and strangers and vary the relationship(s) between the players of a game to observe how kin and ethnic ties influence the willingness of two players to benefit one another at the expense of a third party. We see universal sibling favoritism, but ethnic favoritism, and favoritism toward other in-group members (friends) varies. We argue this may be driven in part by kinship institutions, since favoritism is more common in societies with denser kin networks. ( JEL D9, C9, D73, J12)     

OWN‐NATIONALITY BIAS: EVIDENCE FROM UEFA CHAMPIONS LEAGUE FOOTBALL REFEREES

We examine the existence and magnitude of own‐nationality bias. Using player‐match level data from 12 seasons of the UEFA Champions League (UCL) and referee assignment policies that pair players and referees from the same country, we determine the bias that referees exhibit toward players from their native country. Players officiated by a referee from the same country receive a 10% increase in beneficial foul calls. Referees' own‐nationality bias is more pronounced for national team players, players at home, and in later stages of the tournament. Elite referees exhibit as much, or more, own‐nationality bias as their less experienced counterparts. (JEL L83, J15)     

Ranking opportunity sets: An approach based on the preference for flexibility

We describe a criterion to evaluate subsets of a finite set of alternatives which are considered as opportunity sets. The axioms for set comparison are motivated within the preference for flexibility framework. We assume the preference over the universal set of alternatives to be made of two disjoint binary relations. The result is the axiomatic characterization of a procedure which is formally similar to the leximax ordering, but in our case it incorporates the presence of some uncertainty about the decision-maker final tastes. Received: 20 January 1999/Accepted: 20 October 1999     

100‐Percenting It: Videogame Play Through the Eyes of Devoted Gamers1

We describe salient aspects of the idioculture of videogame play, based on interviews conducted with 20 devoted videogame players and several hours of observation of small‐group game play. We explore the meaningfulness of videogame play for participants, specifically through an examination of the social quality of play, interaction during play, the enactment of status differences in and through play, and players’ desire to play games perfectly and/or completely. We elicit players’ comments about acceptable and unacceptable forms of cheating, and we explore their management of the stigma attached to playing violent games and playing excessively. We conclude by highlighting game players’ penchant for finding moral content in their favorite games and game characters.