Blotto game

[3] Gross and Wagner's 1950[4] research memorandum states Borel's optimal strategy, and coined the fictitious Colonel Blotto and Enemy names.

Borel's game is similar to the above example for very large S, but the players are not limited to round integers.

In the simpler case of two battlefields, Macdonell and Mastronardi 2015 provide the first complete characterization of all Nash equilibria to the canonical simplest version of the Colonel Blotto game.

Nash equilibrium strategies in this version of the game are a set of bivariate probability distributions: distributions over a set of possible resource allocations for each player, often referred to as Mixed Nash Equilibria (such as can be found in Paper-Rock-Scissors or Matching Pennies as much simpler examples).

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.

The same game also finds application in auction theory where bidders must make simultaneous bids.

[7] Several variations on the original game have been solved by Jean-François Laslier,[8] Brian Roberson,[9] and Dmitriy Kvasov.