Endogenous correlated equilibria in noncooperative games

Most of the results of modern game theory presuppose that the choices rational agents make in noncooperative games are probabilistically independent. In this paper I argue that there is noa priori reason for rational agents to assume probabilistic independence. I introduce a solution concept for noncooperative games called anendogenous correlated equilibrium, which generalizes the Nash equilibrium concept by dropping probabilistic independence. I contrast the endogenous correlated equilibrium with the correlated equilibrium defined by Aumann (1974, 1987). I conclude that in general the endogenous correlated equilibrium concept is a more appropriate solution concept for noncooperative game theory than the less general Nash equilibrium concept. I close by discussing the relationship between endogenous correlated equilibrium and the game solution concept calledrationalizability introduced by Bernheim (1984) and Pearce (1984).     

Nash Equilibrium with Lower Probabilities

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible to distinguish between a player's assessment of ambiguity and his attitude towards ambiguity. We also generalize the concept of trembling hand perfect equilibrium. Finally, we demonstrate that for certain attitudes towards ambiguity it is possible to explain cooperation in the one-shot Prisoner's Dilemma in a way that is in accordance with some recent experimental findings.     

Quantitative Assessment of Thriving

We review methodological issues related to the quantitative assessment of thriving with interviews and paper-and-pencil scales. We emphasize two new paper-and-pencil measures of thriving, the Stress-Related Growth Scale (SRGS; Park, Cohen, & Murch, 1996) and the Posttraumatic Growth Inventory (PTGI; Tedeschi & Calhoun, 1996). These scales are designed to assess perceived benefits that result from a specific stressor. Research with the SRGS suggests a unidimensional structure of thriving, whereas research with the PTGI suggests a multidimensional structure. Two possible reasons for this inconsistent finding concern differences in the method of participant selection and in the recall period for the reporting of stressful events. In addition, we present a number of strategies to validate self-report measures of thriving, including corroboration from significant others and the use of control groups. We conclude with a brief discussion of the assessment of thriving at the group and community levels.     

On nonexistence of reconsideration-proof equilibrium with state variables

Reconsideration-proofness is a solution concept proposed by Kocherlakota (Games Econ Behav 15(1):33–54, 1996) for infinite horizon single-player problems in which time inconsistency is important. Kocherlakota’s (1996) definition has a limitation: it is not applicable to environments with state variables. The limitation is important because many time-inconsistent problems have state variables. This paper displays a natural generalization of reconsideration-proofness to environments with state variables, and shows that it leads to nonexistence in three examples. Such nonexistence contrasts with the general existence theorem obtained in environments without state variables in Kocherlakota (1996). In the first two examples, existence can be recovered with a modification in the solution concept. In the last example, nonexistence occurs even with the modified solution concept. Insights about further research are derived from these nonexistence results.     

Challenging passive partnerships with parents and children in the core group forum: a framework for a proactive approach

This paper looks at two concepts central to effective child protection practice: partnerships and the core group system, which need to work together if we are to improve the worrying, ad hoc approaches to child protection work once a child's name has been added to the child protection register. These concepts emerged at around the same point in time, but little has been written about the core group, even though it has been given the key tasks of formulating, implementing and reviewing the child protection plan, and forging effective working partnerships with other professionals, parents/carers and their children ( Calder 1991, 1995 b; Calder & Horwath 1999 ). Whilst the concept of partnership has received considerable media and publishing attention, no previous paper has explored partnerships with families within the core group phase. This reflects the low priority currently afforded to activity following the initial child protection conference, and arguably sets the core group up to fail, even before it has started ( Calder 1996a, 1998 ). The authors draw on their national research into core group practice to explore the notion of partnerships between the core group and parents, carers and children, concluding with some recommendations on how Area Child Protection Committees can create the environment in which we can move from passive to proactive partnerships within a higher profile for this stage and focus of the work. The authors draw on some suggestions from Messages from Research ( Department of Health 1995a ) and from several small-scale research studies into core group practice.     

Joint Beliefs in Conflictual Coordination Games

The traditional solution concept for noncooperative game theory is the Nash equilibrium, which contains an implicit assumption that players probability distributions satisfy t probabilistic independence. However, in games with more than two players, relaxing this assumption results in a more general equilibrium concept based on joint beliefs (Vanderschraaf, 1995). This article explores the implications of this joint-beliefs equilibrium concept for two kinds of conflictual coordination games: crisis bargaining and public goods provision. We find that, using updating consistent with Bayes rule, players beliefs converge to equilibria in joint beliefs which do not satisfy probabilistic independence. In addition, joint beliefs greatly expand the set of mixed equilibria. On the face of it, allowing for joint beliefs might be expected to increase the prospects for coordination. However, we show that if players use joint beliefs, which may be more likely as the number of players increases, then the prospects for coordination in these games declines vis-à-vis independent beliefs.     

An Evolutionary Analysis of Buyer Insurance and Seller Reputation in Online Markets

Applying an evolutionary framework, we investigate how a reputation mechanism and a buyer insurance (as used on Internet market platforms such as eBay) interact to promote trustworthiness and trust in markets with moral hazard problems. Our analysis suggests that the costs involved in giving reliable feedback determine the gains from trade that can be obtained in equilibrium. Buyer insurance, on the other hand, can affect the trading dynamics and equilibrium selection. We find that, under reasonable conditions, buyer insurance crowds out trust, and trustworthiness. Ockenfels gratefully acknowledges the support of the Deutsche Forschungsgemeinschaft. Mengel’s research was supported by the Spanish Ministry of Education and Science (grant SEJ 2004-02172).     

Partial cooperation in strategic multi-sided decision situations

We consider a normal-form game in which there is a single exogenously given coalition of cooperating players that can write a binding agreement on pre-selected actions. The actions representing other dimensions of the strategy space remain under the sovereign, individual control of the players. We consider a standard extension of the Nash equilibrium concept denoted as a partial cooperative equilibrium as well as an equilibrium concept in which the coalition of cooperators has a leadership position. Existence results are stated and we identify conditions under which the various equilibrium concepts are equivalent. We apply this framework to existing models of multi-market oligopolies and international pollution abatement. In a multi-market oligopoly, typically, a merger paradox emerges in the partial cooperative equilibrium. The paradox vanishes if the cartel attains a leadership position. For international pollution abatement treaties, cooperation by a sufficiently large group of countries results in a Pareto improvement over the standard tragedy of the commons outcome described by the Nash equilibrium.     

Applied general equilibrium modeling for long-term energy policy in Germany

The energy model is based on an extension of applied general equilibrium models of the Leontief input-output type, first implemented by Hudson and Jorgenson (1974). One objective of our project is to choose specifications of sectoral production and cost functions that permit us to estimate the unknown parameters of the price functions and input demand functions from a single input-output table in ten energy and 35 non-energy industries. Our second objective is to determine the price for capital and labor as well as the components of final demand endogenously instead of using a separate growth model as an engine for the economic development. Our third objective is to combine the concept of price-dependent substitution within the input structure with the concept of vintage coefficients for the latest plants. By this we incorporate into the input-output analysis the effect on growth as a result of investment, the effect on capacity as a result of new plants, and the effect on prices as a result of new technologies. An application of the model shows the long-term impact on growth and prices under alternative technologies in the electricity industry (nuclear or coal-fired power plants).     

Cultural Stereotypes and Positioning Theory

This paper addresses the application of positioning theory , a new emerging theoretical scheme on the issue of cultural stereotyping. First, a critical conceptual analysis of the words'cultural stereotype'is presented. Secondly, the basic tenets of positioning theory are outlined. Finally, it will be demonstrated how the framework of positioning theory can be used to analytically refine the concept of cultural stereotype. The main upshot of the article is that within social psychology, the concept of cultural stereotype is used in a conceptually vague and blurred way and that, with the necessary conceptual refinements, other research-agendas on stereotypes will have to be tackled if social psychologists want to contribute anything to the societal efforts of changing stereotypes.     

Correlated equilibrium in a nutshell

We analyze the concept of correlated equilibrium in the framework of two-player two-strategy games. This simple framework makes it possible to clearly demonstrate the characteristic features of this concept. We develop an intuitive and easily memorizable test for equilibrium conditions and provide a complete classification of symmetric correlated equilibria in symmetric games.     

A macroeconomic potential describing structural change of the economy

For the purpose of describing change in an economy's structure, and addressing issues of transformation, the notion of a time-dependent macroeconomic potential function is introduced. It penalizes deviations from equilibrium (entrepreneurial error) and induces moves toward equilibrium. Thus, from the concept of a potential function is derived the concept of short-term and long-term change forces. We focus here on the long-term structural changes of an economy as distinct from short-term cyclical variations, and we represent economic transformations as phase-transitions between monostable and ambiguous bistable states of the economy. One important feature of the potential function approach is that the parameter of the potential can be determined from empirical data. In particular, the parameters can be regressed for input variables. Hence, a relationship has been established between the structural change force and a set of input variables, some of which are controlled in part by either public or private sector agents. The method has been applied to West German and United States industry data for 1950–1980.     

Adverse selection,moral hazard and propitious selection

We propose a simple model with preference-based adverse selection and moral hazard that formalizes the cherry picking/propitious selection argument. This argument assumes that individuals differ in risk aversion, potentially resulting in more risk averse agents buying more insurance while being less risky. The propitious selection argument is summarized by two properties: regularity (more risk averse agents exert more caution) and single-crossing (more risk averse agents have a higher willingness to pay for insurance). We show that these assumptions are incompatible with a pooling equilibrium, and that they do not imply a negative correlation between risk and insurance coverage at equilibrium.

Economic Darwinism

We define an evolutionary process of “economic Darwinism” for playing the field, symmetric games. The process captures two forces. One is “economic selection”: if current behavior leads to payoff differences, behavior yielding lowest payoff has strictly positive probability of being replaced by an arbitrary behavior. The other is “mutation”: any behavior has at any point in time a strictly positive, very small probability of shifting to an arbitrary behavior. We show that behavior observed frequently is in accordance with “evolutionary equilibrium”, a static equilibrium concept suggested in the literature. Using this result, we demonstrate that generally under positive (negative) externalities, economic Darwinism implies even more under- (over-)activity than does Nash equilibrium.     

Implementation without rationality assumptions

Hurwicz (Social Choice and public decision making. Essays in honor of Kenneth J. Arrow, Cambridge University Press, Cambridge, 1986) was the first to study an approach to implementation theory based on choice functions instead of preference relations. We argue that the solution concept used by him, the generalized Nash equilibrium, is not really compatible with the idea that individual behavior is describable by a choice function. A new solution concept that better fits the choice function framework is then introduced. Using this, we investigate what behavioral assumptions are needed for the full characterizations of Nash implementable social choice correspondences to still hold. We will show that a condition known as Property α is central.     

Qualitative Heuristics For Balancing the Pros and Cons

Balancing the pros and cons of two options is undoubtedly a very appealing decision procedure, but one that has received scarce scientific attention so far, either formally or empirically. We describe a formal framework for pros and cons decisions, where the arguments under consideration can be of varying importance, but whose importance cannot be precisely quantified. We then define eight heuristics for balancing these pros and cons, and compare the predictions of these to the choices made by 62 human participants on a selection of 33 situations. The Levelwise Tallying heuristic clearly emerges as a winner in this competition. Further refinements of this heuristic are considered in the discussion, as well as its relation to Take the Best and Cumulative Prospect Theory.     

Lost for words

The literature suggests that many children suffer from both emotional and behavioural problems and speech and language difficulties. There are also many children with emotional and behavioural problems who have undetected communication difficulties ( Cohen et al . 1993 ). Undetected communication problems have previously been found in child psychiatric populations ( Giddan et al . 1996 ) and special educational classes for children with emotional and behavioural problems ( Burgess & Bransby 1990 ). A small-scale study reported here also found 'looked after' children who had previously unsuspected communication difficulties. This paper considers why communication problems and emotional and behavioural difficulties often occur together and then reflects on the implications of undetected communication problems for the care of such children. Since communication problems impact on emotional and educational development, there are also suggestions of ways to identify speech and language difficulties in school-age children.     

Correlated Equilibrium in Games with Incomplete Information Revisited

A mistake in “Five legitimate definitions of correlated equilibrium (CE) in games with incomplete information” motivates a re-examination of some extensions of the solution concept that Aumann introduced.     

FORWARD INDUCTION IN GAMES WITH AN OUTSIDE OPTION

We provide eductive foundations for the concept of forward induction, in the class of games with an outside option. The formulation presented tries to capture in a static notion the rest point of an introspective process, achievable from some restricted preliminary beliefs. The former requisite is met by requiring the rest point to be a Nash equilibrium that yields a higher payoff than the outside option. With respect to the beliefs, we propose the Incentive Dominance Criterion. Players should consider one action more likely than another whenever the former is better than getting the outside option for more conjectures over his rival's actions. We apply this model to the case where the subgame is a coordination game with a conflict between payoff dominance and risk dominance. Our results provide support for dominance solvability, but not for Van Damme's notion of forward induction. We show how the forward induction logic helps to select the Pareto dominant equilibrium. This is the case whenever player 1's act of giving up the outside option reverses the incentive dominance relations among 1's pure actions in the subgame.