When two agents hold different priors over an unverifiable state of nature, which affects the outcome of a game they are about to play, they have an incentive to bet on the game's outcome. We pose the following question: what are the limits to the agents' ability to realize gains from such...

What is common to the following situations: designing random incentive schemes to implement team effort, monopoly pricing when consumers are loss averse, arms races when players are privately informed of their armament costs? We present a simple formalism, called X-games, which captures these...