Corresponding contact: dongquan[dot]math[at]gmail[dot]com
Abstract: "The Colonel Blotto game is a famous game commonly used to model resource allocation problems in many domains ranging from security to advertising. Two players distribute a fixed budget of resources on multiple battlefields to maximize the aggregate value of battlefields they win, each battlefield being won by the player who allocates more resources to it. The continuous version of the game---where players can choose any fractional allocation---has been extensively studied, albeit only with partial results to date. Recently, the discrete version---where allocations can only be integers---started to gain traction and algorithms were proposed to compute the equilibrium in polynomial time; but these remain computationally impractical for large (or even moderate) numbers of battlefields. In this paper, we propose an algorithm to compute very efficiently an approximate equilibrium for the discrete Colonel Blotto game with many battlefields. We provide a theoretical bound on the approximation error as a function of the game's parameters. We also propose an efficient dynamic programming algorithm in order to compute for each game instance the actual value of the error. We perform numerical experiments that show that the proposed strategy provides a good approximation to the equilibrium even for a relatively large number of battlefields."
For the use of the code, please read main.R file. These numerical experiments are used to support the results in the paper: [Vu et al., 2018] Dong Quan Vu, Patrick Loiseau, and Alonso Silva. Efficient computation of approximation equilibria in discrete colonel blotto games. In Proc. IJCAI, 2018.
Description of a Colonel Blotto game {CB}(N,m,p):
There are two players, A and B, each has a limited amount of soldiers/troops: m and p respectively (called budgets). There are N battlefields, each one has a value v_i belonging to the bounded range [v_min, v_max]. Simultaneously, two players distribute thier troops towards the battlefields, for example, player A allocates x_A_i troops and player B allocates x_B_i troops to battlefield i. Their allocations have to satisfy the budget constraints, that is the total number of allocated troops does not exceed the total budget (m and p). After allocating, in each battlefield, the player who has higher allocation wins that battlefield and get the corresponding value. In case of a tie, we give the value to player B (or we can use any other tie-breaking rule).