Democracy resolves conflicts in difficult games like Prisoners’ Dilemma and Chicken by stabilizing their cooperative outcomes. It does so by transforming these games into games in which voters are presented with a choice between a cooperative outcome and a Pareto-inferior noncooperative...

In this unusual book, first published by The MIT Press in 1980 and now updated with a new chapter, Steven Brams applies the mathematical theory of games to the Hebrew Bible. Brams's thesis is that God and the human biblical characters acted rationally—that is, given their preferences and their...

Voters today often desert a preferred candidate for a more viable second choice to avoid wasting their vote. Likewise, parties to a dispute often find themselves unable to agree on a fair division of contested goods. In <i>Mathematics and Democracy</i>, Steven Brams, a leading authority in the use of...

Riker's `size principle' predicts that only minimal winning coalitions (MWCs) will form in n-person zero-sum games that satisfy certain conditions. After summarizing the logic of this principle, a model is proposed in which n players can be ordered from most to least weighty. Two different kinds...

Game theory models are ubiquitous in economics, common in political science, and increasingly used in psychology and sociology; in evolutionary biology, they offer compelling explanations for competition in nature. But game theory has been only sporadically applied to the humanities; indeed, we...

A new procedure is proposed for settling disputes which combines binding arbitration (BA) and final-offer arbitration (FOA). Unlike either of the two pure procedures, combined arbitration (CA) induces the two parties to converge in making their final offers. Under BA, the arbitrator's settlement...

A generic Negotiation Game (NG) is used to model a conflict between two parties seeking to resolve their differences and reach a settlement. NG is a 2 × 2 non-constant-sum symmetric game that is `generic' in the sense that its payoffs, which are assumed to be cardinal, are only incompletely...