Allocation Games

Abstract

There are a number of important applications in the economic, military, and political sciences that may be characterized as resource allocation games in which budget‐constrained players strategically allocate resources across multiple simultaneous contests. Partly because it is a foundational problem that is well suited for abstract theoretical modeling, multidimensional strategic resource allocation was one of the first problems examined in modern game theory. Borel (1921) formulates this problem as a constant‐sum game involving two symmetric players who each allocate a fixed amount of resources across a finite number of contests. Each player must distribute their resources without knowing their opponent's distribution of resources. In each of the component contests, the player who allocates the higher level of resources wins the contest, and each player maximizes the sum of the wins across the individual contests. This chapter provides an introduction to this class of games (known as Colonel Blotto games ) with a focus on the intuition for the key results and briefly summarizes several of the recent developments in this literature including: non‐constant‐sum formulations of the Colonel Blotto game, additional restrictions on the strategy space, a simplified form of the Colonel Blotto game, and alternative objectives for the players.

Advertising competitions in social networks

“…Friedman [21] studied the Nash equilibrium and best response function for the asymmetric budgets case with two generals. The case of two generals and where for each distinct value there are at least three battlefields with the same value was stated and solved by Roberson [22] and Shwartz et al [23]. In the context of voting systems, Myerson [24] found the so-lution for the case for equally valued battlefields with ranking scores for any number of candidates.…”