Blotto games
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Blotto games (or Colonel Blotto games, or “Divide a Dollar” games) constitute a class of two-players zero-sum games in which the players are tasked to simultaneously distribute limited resources over several objects (or battlefields). In the classic version of the game, the player devoting the most resources to a battlefield wins that battlefield, and the gain (or payoff) is then equal to the total number of battlefields won.
The Colonel Blotto game was first proposed and solved by Émile Borel in 1921, as an example of a game in which “the psychology of the players matters”. It was studied after the Second World War by scholars in Operation Research, and became a classic in Game Theory. It has been shown that finding a Nash equilibrium, or in other words, the optimal strategies of this game is computationally tractable.
The game is named after the fictional Colonel Blotto from Gross and Wagner’s 1950 paper. The Colonel was tasked with finding the optimum distribution of his soldiers over N battlefields knowing that: 1) on each battlefield the party that has allocated the most soldiers will win, but 2) neither party knows how many soldiers the opposing party will allocate to each battlefield, and: 3) both parties seek to maximize the number of battlefields they expect to win.
This game is commonly used as a metaphor for electoral competition, with two political parties devoting money or resources to attract the support of a fixed number of voters.
See also
Papers
- Gross, O.; Wagner, R. (1950). A Continuous Colonel Blotto Game.
- Roberson, B. (2006). The colonel blotto game. Economic Theory, 29(1), 1-24.
- Ahmadinejad, Mahdi, et al. From Duels to Battefields: Computing Equilibria of Blotto and Other Games. arXiv preprint arXiv:1603.00119