Choosing fair lotteries to defeat the competition
The authors consider the following game: There are \(n\) agents and agent \(i\) is endowed with budget \(b_i\) which is common knowledge. The game consists of two periods. In the first period, each agent (simultaneously) selects any fair lottery over nonnegative real numbers. The lottery is described by its cumulative distribution function \(F(x)\). The lottery \(F_i\) of the agent \(i\) is fair if its expectation is equal to \(b_i\). In the second period, each lottery's outcome is randomly selected according to its corresponding probability distribution. The agent whose outcome is the highest wins. This game is motivated by various real-world settings where the primary goal of every agent is to come out ahead. Such settings include patent races, stock market competitions, R\&D tournaments. The authors show that there is a unique symmetric equilibrium when budgets are equal (so-called ``equal-budget game''). A variant in which the agent can choose his budget at the beginning of the game, and each budget comes at a cost is also considered. This variant is especially natural in many real-world applications where agents must make some initial investments. Another variant where agents do not know the other agents' budgets is also considered.
scientific article; zbMATH DE number 6008664
scientific article