Colonel Blotto

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Website Created by Christopher Wee
PS 391:  Modeling Political Processes
Professor Scott Page
University of Michigan, Ann Arbor

"The clean, precise comparative statics results that game theorists love are not accesible for Blotto.  And yet, as we discuss, this complexity makes Blotto all the more compelling in its interpretations" (Golman 2).

Games of Strategic Mismatch!

Colonel Blotto is a standard game theory model, generally constituting a set of two-player zero sum games, with the payoff dependent on the result of the individual games.
 
The name originated from a fictional colonel named Blotto, who was supposed to optimally place a limited number of soldiers on a given number of fronts under the following assumptions:
 
1) The army with more troops on given front wins that front
2) The army that wins more fronts wins the war
3) Each army does not know how the opponent will allocate troops
4) Implicit Assumptions:
   a. There are more troops than fronts
   b. payoffs: number of fronts won

Basic Colonel Blotto Example
(From Page Lecture)

Imagine a war with three fronts and two armies with one hundred troops each.
 
                                        Front 1          Front 2          Front 3
 
Player One                        34                33                 33
 
Player Two                        40                40                 20
 
In this case, player two wins because he wins 2/3 fronts.  The overall army size does not matter, only the distribution of resources.  Extensions and further examples of this model will be examined from other perspectives on this website.  All in-text citations will be referenced on the "Citations" page.

Sir, what are your orders?

army_reserve_sunset_wp.jpg

How is this different than Prisoner's Dilemma?

In the case of Prisoner's Dilemma, dominant strategies lead to suboptimal outcomes.  On the other hand, in Blotto, we learn about the complexity of strategic mismatch... there is no pure strategy equilibrium!