Communication and its cost in graph-restricted games

We consider cooperative games which are modified by subordination to communication networks. Two players i and j will be able to cooperate only if they pay for the cost w _ij of their communication link (i,j). Coalitions of players are treated similarly and a new characteristic function form game is developed thus. We also examine incentive for players to cooperate in such situations as well as a related index of a player's communicative strength.     

Perceptron versus automaton in the finitely repeated prisoner’s dilemma

We study the finitely repeated prisoner’s dilemma in which the players are restricted to choosing strategies which are implementable by a machine with a bound on its complexity. One player has to use a finite automaton while the other player has to use a finite perceptron. Some examples illustrate that the sets of strategies which are induced by these two types of machines are different and not ordered by set inclusion. Repeated game payoffs are evaluated according to the limit of means. The main result establishes that a cooperation at almost all stages of the game is an equilibrium outcome if the complexity of the machines the players may use is limited enough and if the length T of the repeated game is sufficiently large. This result persists when more than T states are allowed in the player’s automaton. We further consider a variant of the model in which the two players are restricted to choosing strategies which are implementable by perceptrons and prove that the players can cooperate at most of the stages provided that the complexity of their perceptrons is sufficiently reduced.     

Communication Protocols with Belief Messages

This paper presents a communication protocol to reach consensus. In our setting, every player has asymmetric information and evaluates a fixed event on his information. According to the protocol, the sender sends non-partitional messages that he believes the event with a probability of at least his evaluation. We show that the posteriors for the event must be equal among the players after the communication. Journal of Economic Literature Classification: C62, C78.     

A Banzhaf share function for cooperative games in coalition structure

A cooperative game with transferable utility–or simply a TU-game– describes a situation in which players can obtain certain payoffs by cooperation. A value function for these games assigns to every TU-game a distribution of payoffs over the players. Well-known solutions for TU-games are the Shapley and the Banzhaf value. An alternative type of solution is the concept of share function, which assigns to every player in a TU-game its share in the worth of the grand coalition. In this paper we consider TU-games in which the players are organized into a coalition structure being a finite partition of the set of players. The Shapley value has been generalized by Owen to TU-games in coalition structure. We redefine this value function as a share function and show that this solution satisfies the multiplication property that the share of a player in some coalition is equal to the product of the Shapley share of the coalition in a game between the coalitions and the Shapley share of the player in a game between the players within the coalition. Analogously we introduce a Banzhaf coalition structure share function. Application of these share functions to simple majority games show some appealing properties.     

Dynamic focal points in N-person coordination games

To understand how groups coordinate, we study infinitely repeated N-player coordination games in the context of strategic uncertainty. In a situation where players share no common language or culture, ambiguity is always present. However, finding an adequate principle for a common language is not easy: a tradeoff between simplicity and efficiency has to be made. All these points are illustrated on repeated N-player coordination games on m loci. In particular, we demonstrate how a common principle can accelerate coordination. We present very simple rules that are optimal in the space of all languages for m (number of coordination loci) from 2 to 5 and for all N, the number of players. We also show that when more memory is used in the language (strategies), players may not coordinate, whereas this is never the case when players remember only the previous period.     

A test of the Core,Bargaining Set,Kernel and Shapley models in n-person quota games with one weak player

n-person (n – 1)-quota-games where the quotas are positive for certain n – 1 (strong) players and negative for the remaining (weak) player, are discussed. Normative solutions predicted by the Core,the Kernel, the Bargaining Set, the Competitive Bargaining Set, and by the Shapley Value are presented and exemplified.Each of twelve groups of subjects participated in a four-person and a five-person (n – 1)-quota games with one weak player. The weak player was always excluded from the ratified coalition. The division of payoffs among the strong players was more egalitarian than the Kernel solution but less egalitarian than the Shapley value. The Core and the Bargaining Sets were fully supported for the two strongest players, but less supported for the other players. Analyses of the bargaining process confirmed a dynamic interpretation of the Bargaining Set Theory.This research was performed while the author was at the University of North Carolina. The research was partially supported by a PHS Research Grant No. MH-10006 from the National Institute of Mental Health. The author thanks Professor Amnon Rapoport for helpful advice in the design of this study.     

The Longitudinal Interplay between Bullying,Victimization, and Social Status: Age‐related and Gender Differences

The current study examined the longitudinal interplay between bullying, victimization, and social status (acceptance, rejection, and perceived popularity) over the course of 1 year. Cross‐lagged path models were estimated for two cohorts, covering grades 3–6 (N = 3904, M age = 11.2 years) and grades 7–9 (N = 4492, M age = 14.4 years). Comparisons between cohorts and by gender were conducted. The results of this study corroborate the complexity of the longitudinal interplay between bullying, victimization, and social status in showing that direction and strength of associations differ by type of peer status, age, and gender. Conclusions cannot be drawn without taking these differences into account. The findings are discussed according to these differences, and directions for future research are provided.     

Farsightedness and Cautiousness in Coalition Formation Games with Positive Spillovers

We adopt the largest consistent set defined by Chwe (1994; J. Econ. Theory 63: 299–325) to predict which coalition structures are possibly stable when players are farsighted. We also introduce a refinement, the largest cautious consistent set, based on the assumption that players are cautious. For games with positive spillovers, many coalition structures may belong to the largest consistent set. The grand coalition, which is the efficient coalition structure, always belongs to the largest consistent set and is the unique one to belong to the largest cautious consistent set.     

Children in Secure Accommodation

Correspondence to Professor Robert Harris, Pro-Vice-Chancellor, Department of Social Policy and Professional Studies, The University of Hull, Hull HU6 7RX. Summary This paper describes the characteristics of a sample of children(N = 399) being held in secure accommodation in eleven localauthorities prior to the implementation of the Children Act1989. It is argued that secure accommodation cannot be divorcedfrom other aspects of child care policy and practice; that anyconfidence that problems of excessive or variable usage canbe removed by more restrictive legislation is largely misplaced;that when social workers resort to secure accommodation it isoften through a combination of ‘worry’ about anunpredictable child and uncertainty as to what else to do; andthat since not all children in secure accommodation wish toleave it (and the more secure accommodation constitutes goodquality child care the more children are likely to want to stay)a ‘rights’ framework, though necessary, is not asufficient moral or conceptual basis for developing secure accommodationpolicy and practice.     

Not so cheap talk: costly and discrete communication

We model an interaction between an informed sender and an uninformed receiver. As in the classic cheap talk setup, the informed player sends a message to an uninformed receiver who is to take an action which affects the payoffs of both players. However, in our model, the sender can communicate only through the use of discrete messages which are ordered by the cost incurred by the sender. We characterize the resulting equilibria without refining out-of-equilibrium beliefs. Subsequently, we apply an adapted version of the no incentive to separate (NITS) condition to our model. We show that if the sender and receiver have aligned preferences regarding the action of the receiver, then NITS only admits the equilibrium with the largest possible number of induced actions. When the preferences between players are not aligned, we show that NITS does not guarantee uniqueness, and we provide an example where an increase in communication costs can improve communication. As we show, this improvement can occur to such an extent that the equilibrium outperforms the Goltsman et al. (J Econ Theory 144:1397–1420, 2009) upper bound for receiver’s payoffs in mediated communication.     

Secure attachment and social and personality outcomes: The moderating role of emerging adults’ autobiographical memories of parents

Schema-congruent positive autobiographical memories of past experiences with parents, a legacy of secure attachment, may operate jointly with secure attachment to predict social and personality outcomes. The current study examines the moderating role of emerging adults’ autobiographical memories of parents on the relations between maternal and paternal attachment and self-regulation, personal distress, and pathological narcissism. Undergraduates (N = 156, 66.7% female, 53.2% White, M_age = 19.3) completed a battery of measures assessing secure attachment, self-regulation, personal distress, and pathological narcissism (vulnerable and grandiose). Participants were instructed to recall brief autobiographical memories of experiences with their parental figures. Later, they were asked to name the primary emotion associated with each memory. These emotions were coded as positive, negative, or neutral in valence. For the final analysis, a positive emotion index was constructed by subtracting the number of negative memories from the number of positive memories. Regression models simultaneously examining four outcomes (self-regulation, personal distress, and vulnerable and grandiose narcissism) were examined for both female and male parental figures. Interactions between secure attachment and positive memories were only significant for maternal model outcomes. Secure attachment was positively related to self-regulation, and negatively related to personal distress and vulnerable narcissism, when more relative positive memories were recalled. Taken together, this study provides support for the continued influence of secure attachment on social and personality outcomes in emerging adulthood. Further, this influence of secure attachment appears buttressed by readily accessible positive (relative to negative) memories of female attachment figures.     

The Right to Remain Silent

The paper points out that in dynamic games a player may be better-off if other players do not know his choice of strategy. That is, a player may benefit by not revealing (or not pre-determining) the choice of his action in an information set he (thereby) hopes will not be reached. He would be better-off by exercising his ``right to remain silent' if he believes –- as the empirical evidence shows –- that players display aversion to ``Knightian uncertainty'. In this case, a player who behaves strategically, may wish to avoid revealing his strategy. This is true under various interpretations of the notion of ``strategy profiles'.     

Effective choice in the single-shot Prisoner's Dilemma tournament

This paper discusses the results of a single-shot Prisoner's Dilemma computer tournament. In the single-shot Prisoner's Dilemma tournament each pair of players interacts only once. But players can establish and detect reputations because they know how their current opponent has behaved in previous games with other players. The results show that cooperation is worthwhile, even in single-shot games, provided the outcomes of previous games are common knowledge.Reality is a game, but you shouldn't take a game for reality(Pragmaticist Proverb)     

Strategic games with security and potential level players

This paper examines the existence of strategic solutions to finite normal form games under the assumption that strategy choices can be described as choices among lotteries where players have security- and potential level preferences over lotteries (e.g., Cohen, Theory and Decision, 33, 101–104, 1992, Gilboa, Journal of Mathematical Psychology, 32, 405–420, 1988, Jaffray, Theory and Decision, 24, 169–200, 1988). Since security- and potential level preferences require discontinuous utility representations, standard existence results for Nash equilibria in mixed strategies (Nash, Proceedings of the National Academy of Sciences, 36, 48–49, 1950a, Non-Cooperative Games, Ph.D. Dissertation, Princeton University Press, 1950b) or for equilibria in beliefs (Crawford, Journal of Economic Theory, 50, 127–154, 1990) do not apply. As a key insight this paper proves that non-existence of equilibria in beliefs, and therefore non-existence of Nash equilibria in mixed strategies, is possible in finite games with security- and potential level players. But, as this paper also shows, rationalizable strategies (Bernheim, Econometrica, 52, 1007–1028, 1984, Moulin, Mathematical Social Sciences, 7, 83–102, 1984, Pearce, Econometrica, 52, 1029–1050, 1984) exist for such games. Rationalizability rather than equilibrium in beliefs therefore appears to be a more favorable solution concept for games with security- and potential level players.      

Rawlsian Nash solutions

We investigate the conditions which guarantee the choice of Rawlsian solutions by players of unequal maximin positions bargaining under Nash rules. The conditions, viz., subsymmetry and the location of the Pareto set, relate to the structure of the utility set,S.     

Measures of Powerlessness in Simple Games

Consider a simple game with n players. Let ψ_i be the Shapley–Shubik power index for player i. Then 1-ψ_i measures his powerlessness. We break down this powerlessness into two components – a `quixote index' Q <sub>i</sub> (which measures how much of a `quixote' i is), and a `follower index' F <sub>i</sub> (which measures how much of a `follower' he is). Formulae, properties, and axiomatizations for Q and F are given. Examples are also supplied. This revised version was published online in June 2006 with corrections to the Cover Date.     

Tacit Coordination in Choice Between Certain Outcomes in Endogenously Determined Lotteries

Tacit coordination is studied in a class of games in which each of n = 20 players is required to choose between two courses of actions. The first action offers each player a fixed outcome whereas the second presents her the opportunity of participating in a lottery with probabilities that are determined endogenously. Across multiple iterations of the game and trial-to-trial changes in the composition of the lottery, we observe a remarkably good coordination on the aggregate but not individual level. We further observe systematic deviations from the Nash equilibrium solution that are accounted for quite well by a simple adaptive learning model.     

Costly and discrete communication: an experimental investigation

Language is an imperfect and coarse means of communicating information about a complex and nuanced world. We report on an experiment designed to capture this feature of communication. The messages available to the sender imperfectly describe the state of the world; however, the sender can improve communication, at a cost, by increasing the complexity or elaborateness of the message. Here the sender learns the state of the world, then sends a message to the receiver. The receiver observes the message and provides a best guess about the state. The incentives of the players are aligned in the sense that both sender and receiver are paid an amount which is increasing in the accuracy of the receiver’s guess. We find that the size of the language endogenously emerges as a function of the costs of communication. Specifically, we find that higher communication costs are associated with a smaller language. Although the equilibrium predictions do not perform well, this divergence occurs in a manner which is consistent with the experimental communication literature: overcommunication. We find that the sender’s payoffs, relative to equilibrium payoffs, are decreasing in the cost of communication. We also find that the receiver’s payoffs, relative to equilibrium payoffs, are increasing in the cost of communication. Finally, we find imperfections in coordination on the basis of the experimental labels.