Costly force relocation in the Colonel Blotto game
- PDF / 344,351 Bytes
- 14 Pages / 439.37 x 666.142 pts Page_size
- 1 Downloads / 115 Views
Costly force relocation in the Colonel Blotto game Brian Roberson1
· Oz Shy2
Received: 25 February 2019 / Accepted: 27 July 2020 © Society for the Advancement of Economic Theory 2020
Abstract This paper examines a new extensive-form variation of the Colonel Blotto game with two distinct features: (i) in the first stage each player inherits an initial allocation of force across battlefields, which is publicly observable, and (ii) in the second stage it is costly to relocate forces across battlefields. A first-stage pair of allocations of force is said to be stable if there exists an equilibrium of the two-stage game in which neither player relocates any forces from one battlefield to another. We examine the set of stable initial allocations as a function of the implicit and explicit costs of relocating forces. Keywords Colonel Blotto game · Switching cost · Pure strategy equilibrium JEL Classification C72 · D72
1 Introduction The Colonel Blotto game is a two-player normal-form resource-allocation game. Each player is endowed with a level of force which they may allocate across a set of battlefields. In each battlefield, the player that allocates the strictly higher level of force wins that battlefield. In the case of the linear pure-count objective with budget-constrained
The views expressed here are the authors’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System.
B
Oz Shy [email protected] Brian Roberson [email protected]
1
Krannert School of Management, Purdue University, 403 W. State Street, West Lafayette, IN 47907-2056, USA
2
Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree St. NE, Atlanta, GA 30309, USA
123
B. Roberson, O. Shy
use-it-or-lose-it costs,1 the total payoff to each player is linearly increasing in the number of battlefields that the player wins and linearly decreasing in the number of battlefields that the player loses. In this paper, we examine a two-stage Colonel Blotto game. In the first stage, each player inherits an initial allocation of forces across battlefields, which is publicly observable, and in the second stage, it is costly to relocate forces across battlefields. Given the players’ relocations of force, the outcome at each battlefield is determined by the force levels at the end of the second stage. Our interest in the issue of force relocation in the Colonel Blotto game is motivated in part by switching costs issues arising in the industrial organization literature. In that context, switching costs reduce the benefit consumers derive from switching brands, see literature survey in Farrell and Klemperer (2007). Our research is also motivated by relocation issues arising in covering problems such as the maximal covering deployment problem introduced by ReVelle and Rosing (2000).2 The force deployment problem in ReVelle and Rosing (2000) may be described as follows. Consider a set of battlefields that is located on a graph and a single decision maker who is endowed with a level of force that may be allocated
Data Loading...
