I survey and discuss the recent literature on testing experts or probabilistic forecasts, which I would describe as a literature on “strategic hypothesis testing” The starting point of this literature is some surprising results of the following type: suppose that a criterion forjudging...

This chapter reviews developments in the theory of decision making under risk and uncertainty, focusing on models that, over the last 40 years, dominated the theoretical discussions. It also surveys some implications of the departures from the “linearity in the probabilities” aspect of...

Game theory has been employed traditionally as a modeling tool for describing and influencing behavior in societal systems. Recently, game theory has emerged as a valuable tool for controlling or prescribing behavior in distributed engineered systems. The rationale for this new perspective stems...

Aim: To present a systematic development of the theory of combinatorial games from the ground up. Approach: Computational complexity. Combinatorial games are completely determined; the questions of interest are efficiencies of strategies. Methodology: Divide and conquer. Ascend from Nim to Chess...

In one of the most influential existence theorems in mathematics, John F. Nash proved in 1950 that any normal form game has an equilibrium. More than five decades later, it was shown that the computational task of finding such an equilibrium is intractable, that is, unlikely to be carried out...

Population games describe strategic interactions among large numbers of small, anonymous agents. Behavior in these games is typically modeled dynamically, with agents occasionally receiving opportunities to switch strategies, basing their choices on simple myopic rules called revision protocols...

Epistemic game theory formalizes assumptions about rationality and mutual beliefs in a formal language, then studies their behavioral implications in games. Specifically, it asks: what do different notions of rationality and different assumptions about what players believe about…what others...

This chapter reviews the origin and development of game-theoretic ideas in biology. It covers more than half a century of research and focuses on those models and conceptual advancements that are rooted in fundamental biological theory and have been exposed to substantial empirical scrutiny. The...