Robert Aumann's and Thomas Schelling's Contributions to Game Theory: Analyses of Conflict and Cooperation

Advanced information on the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel 2005.Game Theory;

A Dual Model of Cooperative Value

An expanded model of value in cooperative games is presented in which value has either a linear or a proportional mode, and NTU value has either an input or an output basis. In TU games, the modes correspond to the Shapley (1953) and proportional (Feldman (1999) and Ortmann (2000)) values. In NTU games, the Nash (1950) bargaining solution and the Owen- Maschler (1989, 1992) value have a linear mode and an input basis. The egalitarian value (Kalai and Samet (1985)) has a linear mode and an output basis. The output-basis NTU proportional value (Feldman (1999)) and the input-basis variant, identified here, complete the model. The TU proportional value is shown to have a random marginal contribution representation and to be in the core of a positive convex game. The output-basis NTU variant is shown to be the unique efficient Hart and Mas-Colell consistent NTU value based on equal proportional gain in two-player TU games. Both NTU proportional values are shown to be equilibrium payoffs in variations of the bargaining game of Hart and Mas-Colell (1996). In these variations, players' probabilities of participation at any point in the game are a function of their expected payoff at that time. Limit results determine conditions under which players with zero individual worth receive zero value. Further results show the distinctive nature of proportional allocations to players with small individual worths. In an example with a continuum of players bargaining with a monopolist, the monopolist obtains the entire surplus.cooperative game, value, mode, basis, bilateral cooperation, endogenous bargaining power, potential, equal proportional gain, consistency, noncooperative bargaining, zero players, monopoly

The Maximal Payoff and Coalition Formation in Coalitional Games

This paper first establishes a new core theorem using the concept of generated payoffs: the TU (transferable utility) core is empty if and only if the maximum of generated payoffs (mgp) is greater than the grand coalition’s payoff v(N), or if and only if it is irrational to split v(N). It then provides answers to the questions of what payoffs to split, how to split the payoff, what coalitions to form, and how long each of the coalitions will be formed by rational players in coalitional TU games. Finally, it obtains analogous results in coalitional NTU (non-transferable utility) games.Coalition Formation, Core, Maximal Payoff, Minimum No-Blocking Payoff

Lost in Translation? Basis Utility and Proportionality in Games

Cooperative and noncooperative games have no representation of players's basis utilities. Basis utility is the natural reference point on a player's utility scale that enables the determination the marginal utility of any payoff or allocation. A player's basis utility can be determined by an observer and other players under standard rationality assumptions. Basis utility allows interpersonal comparison of proportional utility gains relative to the disagreement outcome. Proportional pure bargaining is the unique solution satisfying efficiency, symmetry, affine transformation invariance and monotonicity in pure bargaining games with basis utility. Characterization of the Nash (1950) bargaining solution requires the assumption of the irrelevance of basis utility in games with basis utility. All existing cooperative solution functions become translation invariant once proper account is taken of basis utility. The noncooperative rationality of these results is demonstrated with a proportional bargaining based on Gul (1988). Further noncooperative application is demonstrated by showing that quantal response equilibria with multiplicative error structures (Goeree, Holt and Palfrey (2004)) become translation invariant with specification of basis utility.Basis utility, equal split, Kalai-Smorodinsky solution, Nash bargaining, quantal response equilibria, proportional bargaining, translation invariance.

Jewish Games for Learning: Renewing Heritage Traditions in the Digital Age

Rather than a discontinuity from traditional modes of learning, new explorations of digital and strategic games in Jewish learning are markedly continuous with ancient practices. An explication of the close connections between traditional modes of Jewish learning, interpretive practice, and gaming culture can help to explain how Jews of the Digital Age can adopt and are adapting modern Games for Learning practices for contemporary purposes. The chapter opens by contextualizing a notion of Jewish Games and the field of Games for Learning. Next, the chapter explains the connections between game systems and Jewish traditions. It closes with a case study of current trends in Jewish Games for Learning in progressive Judaism. How can one view Jewish holidays as heritage game systems? How are texts of the Talmud and the social practice of studying Talmud related to practices of digital and analog games and game play? The Talmud section of the chapter examines rules systems in the Talmud, the theoretical model and case generation of Talmudic sugyot (passages or sections), and the practice of pairs-sacred study, hevruta, in which study partners, sometimes overseen by a senior scholar, seek deeper understanding of the text in a collaborative delving into text and argumentation

"Simply the best (better than all the rest?)" : an investigation into the Booker Prize, 1980-1989, with particular regard to the general rise in business sponsorship of literary awards during the eighties, and the likely effects of the Booker on fiction

The thesis was planned as an attempt to investigate the general increase in the number of literary prizes in the 1980s and particularly those sponsored by business. However it is also an investigation into the specific workings of the Booker Prize as the best known literary award of its kind in Britain, and into the effects that prizes such as the Booker may have had on fiction. Part 1 deals initially with the history and founding of the Booker Prize. Then in Chapter Two it covers some of the broader issues involving literary awards in general, such as the tendency among them to encourage a conflation of business and aesthetic ideals. Part 2 deals with the issue of patronage for the arts and with the predominance of particular social groups among the authors, judges and members of the Management Committee of the Booker Prize. I also examine how certain types of supposedly aesthetic evaluations arise and how they subsequently come to predominate. In the final part of the thesis I look at the issue of standardisation as it relates to the novels which won the Booker Prize during the 1980s

Herbert Scarf: a Distinguished American Economist

Herbert Eli Scarf (born on July 25, 1930 in Philadelphia, PA) is a distinguished American economist and Sterling Professor (Emeritus as of 2010) of Economics at Yale University. He is a member of the American Academy of Arts and Sciences, the National Academy of Sciences and the American Philosophical Society. He served as the president of the Econometric Society in 1983. He received both the Frederick Lanchester Award in 1973 and the John von Neumann Medal in 1983 from the Operations Research Society of America and was elected as a Distinguished Fellow of the American Economic Association in 1991.