Coalitional Interval Games for Strategic Games in Which Players Cooperate

We propose a method to associate a coalitional interval game with each strategic game. The method is based on the lower and upper values of finite two-person zero-sum games. Associating with a strategic game a coalitional interval game we avoid having to take either a pessimistic or an optimistic approach to the problem. The paper makes two contributions to the literature: It provides a theoretical foundation for the study of coalitional interval games and it also provides, studies, and characterizes a natural method of associating coalitional interval games with strategic games.      

On the emptiness of the stability set of order d

We know from Li's theorem (1993) that the stability set of order d may be empty for some preference profiles. However, one may wonder whether such situations are just rare oddities or not. In this paper, we partially answer this question by considering the restrictive case where the number of alternatives is the smallest compatible with an empty stability set. More precisely, we provide an upper bound on the probability for having an empty stability set of order d for the majority game under the Impartial Weak Ordering Culture assumption. This upper bound is already extremely low for small population and tends to zero as the number of individuals goes to infinity.     

Leadership and the effective choice of information regime

Economic research suggests that, in some circumstances, exogenously restricting the information leaders can provide to followers can overcome the free-riding problem and coordination failures, and improve efficiency in collective actions. The reason is that a leader’s information advantage can deprive followers of the information necessary for profitable defection. In this paper, we focus on situations where the decision to restrict access to information is an endogenous choice made by the leader. We experimentally investigate if leaders choose to strategically withhold information when appropriate to improve outcomes. To address this question, we adopt a single-shot collective action game in which a leader–follower setting with information advantage for the leader can potentially solve the free-riding problem and coordination failures. Our results suggest that leaders, in many circumstances, fail to utilize their information advantage to improve efficiency. This implies that groups may benefit if a nontransparent information regime is exogenously imposed on them.     

Hyperplane games,prize games and NTU values

The Shapley value is a well-known solution concept for TU games. The Maschler–Owen value and the NTU Shapley value are two well-known extensions of the Shapley value to NTU games. A hyperplane game is an NTU game in which the feasible set for each coalition is a hyperplane. On the domain of monotonic hyperplane games, the Maschler–Owen value is axiomatized (Hart Essays in game theory. Springer, 1994). Although the domain of hyperplane game is a very interesting class of games to study, unfortunately, on this domain, the NTU Shapley value is not well-defined, namely, it assigns an empty set to some hyperplane games. A prize game (Hart Essays in game theory. Springer, 1994) is an NTU game that can be obtained by “truncating” a hyperplane game. As such, a prize game describes essentially the same situation as the corresponding hyperplane game. It turns out that, on the domain of monotonic prize games, the NTU Shapley value is well-defined. Thus, one can define a value which is well-defined on the domain of monotonic hyperplane games as follows: given a monotonic hyperplane game, first, transform it into a prize game, and then apply the NTU Shapley value to it. We refer to the resulting value as the “generalized Shapley value” and compare the axiomatic properties of it with those of the Maschler–Owen value on the union of the class of monotonic hyperplane games and that of monotonic prize games. We also provide axiomatizations of the Maschler–Owen value and the generalized Shapley value on that domain.

     

Measuring Support Provisions for People Living With Disabilities in South Asia: An Accessibility Index

ABSTRACT

The terms “empowerment,” “rights,” and “inclusiveness” are now commonly used in public policy, but little emphasis is placed on “accessibility” issues in the integration of disabled people. This article proposes a composite index to measure economic support provisions, such as employment, vocational training, microfinance, and safety nets. The index was tested in a case study (N= 245) of two districts in Pakistan. Results support a “cost/benefit”-based philosophy, rather than the “means–ends” goal, where the disabled poor are viewed as unproductive and risky payers, instead of giving them an opportunity to exercise their potential. Change for the disadvantaged poor can be brought about with the mandatory use of this index in local annual audits. Future research might examine the impact of the index and standardize it for global use.     

Are game theoretic concepts suitable negotiation support tools? From Nash equilibrium refinements toward a cognitive concept of rationality

If game theory is to be used as a negotiation support tool, it should be able to provide unambiguous recommendations for a target to aim at and for actions to reach this target. This need cannot be satisfied with the Nash equilibrium concept, based on the standard instrumental concept of rationality. These equilibria, as is well known, are generally multiple in a game. The concept of substantive or instrumental rationality has proved to be so pregnant, however, that researchers, instead of re-evaluating its use in game theory, have simply tried to design concepts related to the Nash equilibrium, but with the property of being unique in a game — i.e., they have devised ways ofselecting among Nash equilibria. These concepts have been labeledrefined Nash equilibria. The purpose of this paper is to show the following.

1. The different types of refined Nash equilibria, based on the principle of backward induction, can lead to severe contradictions within the framework itself. This makes these concepts utterly unsatisfactory and calls for a new appraisal of the reasoning process of the players.
2. The degree of confidence in the principle of backward induction depends upon the evaluation of potential deviations with respect to the extended Nash equilibrium concept used and upon the possible interpretations of such deviations by the different players. Our goal is to show that the nature of these possible interpretations reinforces the argument that a serious conceptual reappraisal is necessary.
3. Some form of forward induction should then become the real yardstick of rationality, extending Simonianprocedural rationality towards the concept ofcognitive rationality. This could open the way to a renewed game theoretic approach to negotiation support systems. Such a research program, which would be a revision of the basic game theoretic concepts, is dealt with in the end of the paper.

     

Punishing greediness in divide-the-dollar games

Brams and Taylor 1994 presented a version of the divide-the-dollar game (DD), which they call DD1. DD1 suffers from the following drawback: when each player demands approximately the entire dollar, then if the least greedy player is unique, then this player obtains approximately the entire dollar even if he is only slightly less greedy than the other players. I introduce a parametrized family of 2-person DD games, whose “endpoints” (the games that correspond to the extreme points of the parameter space) are (1) a variant of DD1, and (2) a game that completely overcomes the greediness-related problem. I also study an n-person generalization of this family. Finally, I show that the modeling choice between discrete and continuous bids may have far-reaching implications in DD games.     

Information aggregation and preference heterogeneity in committees

This paper is concerned with the efficiency of information aggregation in a committee whose members have heterogeneous preferences over a binary decision variable. We study a voting game with a pre-vote communication stage and identify conditions under which full information aggregation is possible. In particular, if preferences are common knowledge and each committee member is endowed with information, full information aggregation is possible despite preference heterogeneity.     

Socially Structured Games

We generalize the concept of a cooperative non-transferable utility game by introducing a socially structured game. In a socially structured game every coalition of players can organize themselves according to one or more internal organizations to generate payoffs. Each admissible internal organization on a coalition yields a set of payoffs attainable by the members of this coalition. The strengths of the players within an internal organization depend on the structure of the internal organization and are represented by an exogenously given power vector. More powerful players have the power to take away payoffs of the less powerful players as long as those latter players are not able to guarantee their payoffs by forming a different internal organization within some coalition in which they have more power. We introduce the socially stable core as a solution concept that contains those payoffs that are both stable in an economic sense, i.e., belong to the core of the underlying cooperative game, and stable in a social sense, i.e., payoffs are sustained by a collection of internal organizations of coalitions for which power is distributed over all players in a balanced way. The socially stable core is a subset and therefore a refinement of the core. We show by means of examples that in many cases the socially stable core is a very small subset of the core. We will state conditions for which the socially stable core is non-empty. In order to derive this result, we formulate a new intersection theorem that generalizes the KKMS intersection theorem. We also discuss the relationship between social stability and the wellknown concept of balancedness for NTU-games, a sufficient condition for non-emptiness of the core. In particular we give an example of a socially structured game that satisfies social stability and therefore has a non-empty core, but whose induced NTU-game does not satisfy balancedness in the general sense of Billera.      

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.     

Internalizing the public cost of obesity in Spain: Distributional effects on nutrient intake

Studies dealing with obesity have confronted it either from the fiscal policy or from economic cost perspective. There is the need to target fiscal policy goals at the economic cost that obesity imposes on society instead of simulating arbitrary taxes schemes. This paper analyzes the effectiveness of imposing a revenue-neutral fat tax in Spain addressed to internalize the public health expenditure associated to obesity. Results suggest that this tax policy led to an improvement in the diet quality, and decreased the consumption of saturated fatty acid, sodium, and cholesterol. From the welfare perspective, the tax is regressive across all household segments.     

Implementing equal division with an ultimatum threat

We modify the payment rule of the standard divide the dollar (DD) game by introducing a second stage and thereby resolve the multiplicity problem and implement equal division of the dollar in equilibrium. In the standard DD game, if the sum of players’ demands is less than or equal to a dollar, each player receives what he demanded; if the sum of demands is greater than a dollar, all players receive zero. We modify this second part, which involves a harsh punishment. In the modified game \((D\!D^{\prime })\) , if the demands are incompatible, then players have one more chance. In particular, they play an ultimatum game to avoid the excess. In the two-player version of this game, there is a unique subgame perfect Nash equilibrium in which players demand (and receive) an equal share of the dollar. We also provide an \(n\) -player extension of our mechanism. Finally, the mechanism we propose eliminates not only all pure strategy equilibria involving unequal divisions of the dollar, but also all equilibria where players mix over different demands in the first stage.     

Resolving the Trust Predicament: A Quantum Game-theoretic Approach

Developing a good theoretical understanding of the role of trust in IR (such as in the events leading to the end of the Cold War) is still an open problem. Most game-theoretic studies of trust do not go beyond the limitations of an (ontologically) individualistic paradigm, thus assuming a pre-defined set of individual strategies. Yet, it is a fact that the predicament of collective trust is empirically resolved in many situations. This paper suggests a new game-theoretic approach—Quantum Game Theory (QGT)—to understand and explain how the predicament of trust is resolved. In a quantum game of trust the actors play the game by simultaneously collectively reconstructing the strategic environment in such a way as to become mutually strategically entangled. Quantum strategic entanglement allows trust to emerge between the two actors without assuming a need for signaling, prior “contract” type of arrangement, or any form of third-party communication. The paper develops and solves such a model of quantum game of trust     

Human Relations Training in Schools and Elsewhere

Human relations training in many forms, the best known of which are encounter groups, enjoys wide popularity in industry, government and education. Some ‘professional’ objections to the running of such groups are raised, and it is proposed that these objections may be partially answered if there is a non-profit-making national association of group leaders whose function would be to provide a code of ethics to members and information to the public. As well as these professional objections involving the areas of leadership, screening and casualties, there are also objections to the 'process' of groups itself; to these latter objections arising out of an individual's sensibility and subjective interpretations of events, no compelling reply can be given. Affirmation of the interactions in encounter groups is likewise a subjective matter.     

A choice for ‘me’ or for ‘us’? Using we-reasoning to predict cooperation and coordination in games

Cooperation is the foundation of human social life, but it sometimes requires individuals to choose against their individual self-interest. How then is cooperation sustained? How do we decide when instead to follow our own goals? I develop a model that builds on Bacharach (in: Gold, Sugden (eds) Beyond individual choice: teams and frames in game theory, 2006) ??circumspect we-reasoning?? to address these questions. The model produces a threshold cost/benefit ratio to describe when we-reasoning players should choose cooperatively. After assumptions regarding player types and beliefs, we predict how the extent of cooperation varies across games. Results from two experiments offer strong support to the models and predictions herein.     

Domination structures and multicriteria problems in n-person games

Multiple criteria decision problems with one decision maker have been recognized and discussed in the recent literature in optimization theory, operations research and management science. The corresponding concept with n-decision makers, namely multicriteria n-person games, has not yet been extensively explored.In this paper we first demonstrate that existing solution concepts for single criterion n-person games in both normal form and characteristic function form induce domination structures (similar to those defined and studied by Yu [39] for multicriteria single decision maker problems) in various spaces, including the payoff space, the imputation space and the coalition space. This discussion provides an understanding of some underlying assumptions of the solution concepts and provides a basis for generalizing and generating new solution concepts not yet defined. Also we illustrate that domination structures may be regarded as a measure of power held by the players.We then illustrate that a multicriteria problem can naturally arise in decision situations involving (partial) conflict among n-persons. Using our discussion of solution concepts for single criterion games as a basis, various approaches for resolving both normal form and characteristic function form multicriteria n-person games are proposed. For multicriteria games in characteristic function form, we define a multicriteria core and show that there exists a single game point whose core is equal to the multicriteria core. If we reduce a multicriteria game to a single criterion game, domination structures which are more general than classical ones must be considered, otherwise some crucial information in the game may be lost. Finally, we discuss a parametrization process which, for a given multicriteria game, associates a single criterion game to each point in a parametric space. This parametrization provides a basis for the discussion of solution concepts in multicriteria n-person games.     

Toward increased public representation on bioethics committees: Lessons from Judging the cold war human radiation experiments∗

The process of judging the Cold War Human Radiation Experiments illuminates a need to develop a model for an appropriate public role on bioethics committees. A citizen representative was appointed to the President's Advisory Committee on Human Radiation Experiments, and the Committee solicited broad public participation in their investigation. However, many members of the affected and interested public desired further representation on the Committee, as they tended towards stronger ethical condemnations of the experiments than the Committee expressed. I offer an account of a testimony before the Committee by a radiation experiment subject's survivor to illustrate this contrast in moral perspective. I consider some the contributions that “non‐expert”; public members can add to committee deliberations, and suggest that concerns about public representatives may be overcome with the guidance of clearer principles for selecting public members. Further efforts to increase membership by the general and affected public on bioethics committees will enhance deliberations and help realize the democratic ideals of bioethics.     

Location of Public Goods and the Calculus of Voting: The Seattle Monorail Referendum*

Objectives. In this article we explore how the geographic location of a proposed public good on the ballot in a local referendum influences voting turnout. We argue that voters who live farther away from the good, and are thus likely to bear the cost of the good but have no access to it, would be more motivated to turn out in the election. Drawing on the cost‐orientation hypothesis, or negativity effect, “that people are more strongly motivated to avoid losses than to approach gains,” we expect these voters to derive higher expressive benefits from the act of voting relative to those of voters located closer to the good. Methods. We examine voting turnout in the 2002 referendum in the City of Seattle on the proposed construction of a monorail. We conduct our study at the precinct level using spatial tools of analysis. We evaluate the effect of accessibility on turnout by means of a curvilinear model that incorporates demographic and political variables. Results. We find that voting turnout is determined partly by accessibility. Turnout is higher in precincts located farther away from the monorail line than in precincts located relatively closer to the line. Partisanship conditions this effect. Conclusions. This study provides tentative support for linking voter turnout to the negativity effect via expressive benefits. Voters' location in relation to a public good may affect directly their political behavior by means of their perceived net gains or losses from the good.     

Hoarding in the Community: A Code Enforcement and Social Service Perspective

ABSTRACT

Hoarding behaviors endanger individuals and their communities. Although there is a growing literature on clinically referred and elderly hoarders, there is limited information about hoarding behaviors beyond these contexts. This study examines the frequency, characteristics, and outcomes of cases involving hoarding encountered by code enforcement officials and social service staff. Prior to an in-service training, 236 social service staff members completed a 43-item survey about their experiences with cases involving hoarding. Respondents reported encountering between two and three cases per year. Although these hoarding cases were estimated to cost more than $3,700 in cleaning fees, 83% of respondents reported having received no prior training on dealing with hoarding. Survey responses suggested that hoarding situations were difficult to resolve and involved multiple community agencies. Collectively, hoarding behaviors appear to be a problem regularly encountered by social service members, who often serve as the initial point of contact. Along with increased training, future research is needed to develop and evaluate collaborative interagency protocols to manage this multifaceted problem. Empirically informed interagency protocols may facilitate the timely referral of community hoarders to mental health professionals and may lead to improved outcomes.     

Stubbornness,Power, and Equilibrium Selection in Repeated Games with Multiple Equilibria

Axelord’s [(1970), Conflict of Interest, Markham Publishers, Chicago] index of conflict in 2 × 2 games with two pure strategy equilibria has the property that a reduction in the cost of holding out corresponds to an increase in conflict. This article takes the opposite view, arguing that if losing becomes less costly, a player is less likely to gamble to win, which means that conflict will be less frequent. This approach leads to a new power index and a new measure of stubbornness, both anchored in strategic reasoning. The win probability defined as power constitutes an equilibrium refinement which differs from Harsanyi and Selten’s [(1988), A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge] refinement. In contrast, Axelrod’s approach focuses on preferences regarding divergences from imaginary outmost rewards that cannot be obtained jointly. The player who is less powerful in an asymmetric one-shot game becomes more powerful in the repeated game, provided he or she values the future sufficiently more than the opponent. This contrasts with the view that repetition induces cooperation, but conforms with the expectation that a more patient player receives a larger share of the pie.