A note on the paradox of smaller coalitions

We consider hedonic coalition formation games that are induced by a simple TU-game and a cooperative solution. For such models, Shenoy’s (Int J Game Theory 8:133–164, 1979) absence of the paradox of smaller coalitions provides a sufficient condition for core existence. We present three different versions of his condition in order to compare it to the top coalition property of Banerjee et al. (Social Choice Welfare 18:135–153, 2001) that guarantees nonemptiness of the core in more general models. As it turns out, the top coalition property implies a condition in which Shenoy’s paradox is not present for at least one minimal winning coalition. Conversely, if for each non-null player Shenoy’s paradox is not present for at least one minimal winning coalition containing that player, then the induced hedonic game satisfies the top coalition property.     

Losses Disguised as Wins Affect Game Selection on Multiline Slots

Multiline slots are exciting games that contain features which make them alluring. One such feature is a loss disguised as a win (LDW); wherein, players win less than they wager (e.g., bet 2 dollars, win back 50 cents), but this net loss is disguised by flashing graphics and winning sounds. Research to date concludes that LDWs are both rewarding and reinforcing. Here, we investigated whether LDWs affect players’ game selection. Thirty-two undergraduate students with experience playing slot machines played 100 spins on four games—two had positive payback percentages (115%) and two had negative payback percentages (85%) after 100 spins. For each payback percentage condition, there was a game with no LDWs and a game with a moderate number of LDWs. For the 100 spins, players could choose to play whichever game they wished. They then rated their preference for each game following the 100-spins and chose a game to continue playing. The majority of players preferred playing the positive payback percentage game with LDWs and chose to continue playing this game over the three other games. We conclude that in addition to LDWs being reinforcing and rewarding, LDWs do in fact influence game selection. We conclude that responsible gambling initiatives should educate players about LDWs.     

Core in a simple coalition formation game

We analyze the core of a class of coalition formation game in which every player's payoff depends only on the members of her coalition. We first consider anonymous games and additively separable games. Neither of these strong properties guarantee the existence of a core allocation, even if additional strong properties are imposed. We then introduce two top-coalition properties each of which guarantee the existence. We show that these properties are independent of the Scarf-balancedness condition. Finally we give several economic applications. Received: 31 July 1999/Accepted: 5 January 2000     

Social and Psychological Challenges of Poker

Poker is a competitive, social game of skill and luck, which presents players with numerous challenging strategic and interpersonal decisions. The adaptation of poker into a game played over the internet provides the unprecedented opportunity to quantitatively analyze extremely large numbers of hands and players. This paper analyzes roughly twenty-seven million hands played online in small-stakes, medium-stakes and high-stakes games. Using PokerTracker software, statistics are generated to (a) gauge the types of strategies utilized by players (i.e. the ‘strategic demography’) at each level and (b) examine the various payoffs associated with different strategies at varying levels of play. The results show that competitive edges attenuate as one moves up levels, and tight-aggressive strategies––which tend to be the most remunerative––become more prevalent. Further, payoffs for different combinations of cards, varies between levels, showing how strategic payoffs are derived from competitive interactions. Smaller-stakes players also have more difficulty appropriately weighting incentive structures with frequent small gains and occasional large losses. Consequently, the relationship between winning a large proportion of hands and profitability is negative, and is strongest in small-stakes games. These variations reveal a meta-game of rationality and psychology which underlies the card game. Adopting risk-neutrality to maximize expected value, aggression and appropriate mental accounting, are cognitive burdens on players, and underpin the rationality work––reconfiguring of personal preferences and goals––players engage into be competitive, and maximize their winning and profit chances.     

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     

Spoilers,blocking coalitions,and the core

This paper surveys non-cooperative implementations of the core which tell an intuitive story of coalition formation. Under the core solution concept, if a blocking coalition exists those agents abandon the current allocation without regard for the consequences to players outside the blocking coalition. Yet in certain circumstances, these players have an incentive to prevent formation of any blocking coalition; a game analyzed in Lagunoff (Games Econ Behav 7:54–61, 1994) is vulnerable to such circumstances. To obtain all core allocations and only core allocations, a mechanism must either restrict the actions of non-members of a proposed coalition, or ensure that non-members are unharmed by the departure of the coalition. These requirements illustrate the core’s nonchalance toward agents not in blocking coalitions. The author gives special thanks to Beth Allen and Andy McLennan for their direction, and gratefully acknowledges valuable discussions with Roger Lagunoff, Hugo Sonnenschein, John Ledyard, Myrna Wooders, Nuray Akin, as well as comments from participants at the 2004 Spring Midwest Economic Theory and the Society for Economic Design conferences and from anonymous referees. All errors remain my own. Partial funding came from National Science Foundation grants DMI-0070257 and DMI-0217974.     

Perceived harmony,similarity and cooperation in 2 × 2 games: An experimental study

Game harmony is a generic game property describing how conflictual or non-conflictual the interests of players are. Simple and general game harmony measures can predict mean cooperation in 2 × 2 games such as the Prisoner’s Dilemma, the Chicken and trust games. Two measures can be simply computed from monetary payoffs; another, the similarity index, can also be justified by theories of similarity-based reasoning. When data from Oxford and Frankfurt–Oder are disaggregated across experiments, countries and learning history, and when the similarity index is a valid measure, parsimonious regressions can explain around half of the variance in mean cooperation rates.     

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.     

An axiomatization of the core for finite and continuum games

We provide a new axiomatization of the core of games in characteristic form. The games may have either finite sets of players or continuum sets of players and finite coalitions. Our research is based on Peleg's axiomatization for finite games and on the notions of measurement-consistent partitions and the f-core introduced by Kaneko and Wooders. Since coalitions are finite in both finite games and in continuum games, we can use the reduced game property and the converse reduced game property for our axiomatization. Both properties are particularly appealing in large economies.This paper is a revision of University of Bonn Sonderforschungsbereich 303 Discussion Paper No. B-149, with the same title.     

Group payoffs as public signals

We study experimentally the effect on individual behavior of comparative, but payoff-irrelevant, information in a near-minimal group setting. Specifically, in each round, group members see the groups’ cumulative payoffs, which consist of an aggregation of the earnings of each member of the group in the round. Our novel experimental design incorporates two games (the Trust game and the Dictator game) whose payoffs are carefully chosen to ensure cross-game comparability. In the baseline, no comparative information is displayed; the sessions are otherwise identical.Our first set of results shows that the display is sufficient to induce an in-group bias, which can neither be attributed to mere categorization of subjects into groups nor to a stronger sense of group identity as a result of the display. Moreover, we corroborate existing results, which find that, relative to the baseline, the display is welfare reducing in the Trust game. Our second set of results shows that when comparing the allocators’ decisions across the two games, a first mover’s trust is reciprocated by the second mover independently of group identity.     

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     

BECAUSE IT'S FREE POKER! A QUALITATIVE ANALYSIS OF FREE TEXAS HOLD'EM POKER TOURNAMENTS

The game of poker has dramatically increased in popularity in America over the past decade, and includes a new trend in poker in which tournaments are played with no monetary wagering. These “free” poker tournaments are the primary focus of this project. Our interest in these free poker tournaments was twofold: first, we wished to identify what would motivate a person to play poker when there is no profit motive; second, we wanted to learn how the social dynamics of the game itself may or may not change when monetary risk is not present. Through covert participant observation of free poker tournaments at four different locations we were able to discover three main motivations among the players: sharpening skills for later cash games, sociability, and gaining the status of a “regular player.” We also discovered that the tenor and tempo of the game tended to vary not as a function of the location, but rather because of the social class of the players. We offer several hypotheses to guide future research endeavors in this area.     

Criticality in games with multiple levels of approval

In this article, criticality within a voting game is rigorously defined and examined. Criticality forms the basis of the traditional voting power measures frequently employed to analyse voting games; therefore understanding criticality is a pre-requisite to understanding any such analysis. The concept of criticality is extended to encompass games in which players are allowed to express multiple levels of approval. This seemingly innocuous extension raises some important questions, forcing us to re-evaluate exactly what it means to be critical. These issues have been largely side-stepped by the main body of research as they focus almost exclusively on ‘yes/no’ voting games, the so called single level approval voting games. The generalisation to multilevel approval voting games is much more than just a theoretical extension, as any single level approval game in which a player can abstain is in effect a multilevel approval voting game.     

Hierarchy of players in swap robust voting games

Ordinarily, the process of decision making by a committee through voting is modeled by a monotonic game the range of whose characteristic function is restricted to {0, 1}. The decision rule that governs the collective action of a voting body induces a hierarchy in the set of players in terms of the a-priori influence that the players have over the decision making process. In order to determine this hierarchy in a swap robust game, one has to either evaluate a power index (e.g., the Shapley–Shubik index, the Banzhaf–Coleman index) for each player or conduct a pairwise comparison between players, whereby a player i is ranked higher than another player j if there exists a coalition in which i is more desirable as a coalition partner than j. In this paper, we outline an alternative mechanism to determine the ranking of players in terms of their a-priori power. This simple and elegant method uses only minimal winning coalitions, rather than the entire set of winning coalitions.     

Subject-specific performance information can worsen the tragedy of the commons: Experimental evidence

The main aim of this article is to investigate the behavioral consequences of the provision of subject-specific information in the group effort levels chosen by players in an experimental CPR game. We examine two basic treatments, one with incomplete information and the other with complete information. In the former, subjects are informed only about their own individual payoffs and the aggregate extraction effort level of the group, and in the latter they are also informed about the individual effort levels and payoffs of each subject. Given this setting, the basic question we attempt to answer is: Will the provision of subject-specific performance information (i.e. individual’s effort levels and payoffs) improve or worsen the tragedy of the commons (i.e. an exploitation effort level greater than the socially optimum level)? In order to motivate our hypotheses and explain our experimental results at the individual level, we make use of the theory of learning in games, which goes beyond standard non-cooperative game theory, allowing us to explore the three basic benchmarks in the commons context: Nash equilibrium, Pareto efficient, and open access outcomes. We use several learning and imitation theoretical models that are based on contrasting assumptions about the level of rationality and the information available to subjects, namely: best response, imitate the average, mix of best response and imitate the average, imitate the best and follow the exemplary learning rules. Finally, in order to econometrically test the hypotheses formulated from the theoretical predictions we use a random-effects model to assess the explanatory power of the different selected behavioral learning and imitation rules.     

Probabilistic cheap talk

We consider a model in which there is uncertainty over when a one-shot game will be played. We show how a mechanism designer can implement desirable outcomes in certain economic games by manipulating only the probability that the game is played in a given round while leaving all other aspects of the game unchanged. We also show that if there is no discounting, this uncertainty imparts a sequential structure that is almost mathematically equivalent to a repeated version of the game with discounting. In particular, a folk theorem applies to such games. Thus, games of probabilistic cheap provide a third interpretation of the repeated game framework with the additional feature that expected payoff is invariant to the probability of the game ending. Received: 10 May 1999/Accepted: 16 October 2000     

Gamson’s law and hedonic games

This note adds one celebrated coalition formation game due to Gamson (Am Soc Rev 26:373–382 1961a, Am Soc Rev 26:565–573, 1961b) in the list of applications of the theory of hedonic games explored by Banerjee et al. (Soc Choice Welf 18:135–153, 2001) and Bogomolnaia and Jackson (Games Econ Behav 38: 204–230, 2002). We apply their results to study the original Gamson game and offer extensions both to a multi-dimensional characteristics space and to an infinite number of players.     

Fully-Revealing Equilibria of Multiple-Sender Signaling and Screening Models

Models of incomplete information have played a major role in the fields of political science and political economy. The models have almost exclusively been signaling models, and their substantive focus is frequently on situations in which the extensive form is not dictated by institutional requirements or procedures. We explore the relation between multiple-sender signaling games and the corresponding screening or mechanism design games without transfers and establish an equivalence result. If there is a fully-revealing equilibrium in the signaling game there is also a full-information optimal mechanism that yields the principal’s optimal policy in every state. The converse, that fully-revealing equilibria exist in the signaling game if a full-information optimal mechanism exists, is true if and only if the mechanism involves only the selection of policies that are optimal for some belief about the state. We also present two straightforward sufficient conditions for the existence of full-information optimal mechanisms. When either holds, fully-revealing equilibria in the signaling and screening games exist. The perceived advantage of the signaling over the screening approach – that no commitment by the principal is assumed – may be over-stated as flexibility in specifying off the path beliefs can mimic commitment.     

The rationalization process of online game cheating behaviors

Online deviant behaviors have been prevalent since the Internet became ubiquitous, but research in this field is relatively scarce. The present study investigates a unique deviant behavior in online video gaming communities – game cheating – to further understand the scope of online deviant social behaviors. This paper aims to uncover how game players actively create and negotiate new meanings of game cheating in online games. Six focus groups were conducted to explore the rationalization process for engaging in game cheating among players of different online video games. It was discovered that elements of intentionality, utility, core gaming goals, evolving gaming norm, and social ties to gaming communities serve as important rationalizing process to justify game cheating behaviors. Through the discovery of these mental schemas for online game cheating, the paper discusses how online deviant behaviors are connected with social life online and form a unique online culture.     

STRUCTURAL ESTIMATION OF SEQUENTIAL GAMES OF COMPLETE INFORMATION

In models of strategic interaction, there may be important order of entry effects if one player can credibly commit to an action (e.g., entry) before other players. If one estimates a simultaneous‐move model, then the move‐order effects will be confounded with the payoffs. This article considers nonparametric identification and simulation‐based estimation of sequential games of complete information. Relative to simultaneous‐move games, these models avoid the problem of multiple equilibria and require fewer payoff normalizations. We apply the estimator in several Monte Carlo experiments and to study entry‐order effects using data from the airline industry. (JEL C57, C15, L93)