Maria Montero, Alex Possajennikov, Martin Sefton and Theodore L. Turocy
How should a player allocate a fixed amount of resources across several issues while in competition with another player? The original story for this situation had two army commanders allocating troops across battlefields (hence the name “Colonel Blotto game”), but the setting is applicable to other decisions such as a firm competing in several markets, or a politician distributing campaign funds across several voting districts. If the issues have different values, it is clear that more valuable issues should be favoured relative to less valuable ones. But by how much? If one issue is worth twice as much as another, should it command twice as many resources? Since each player aims to win in a majority of issues (weighted by their value), should they concentrate their resources on a group of issues that would be just sufficient to win the contest, or should they spread their resources more widely?
In this Nottingham School of Economics working paper, published in Economic Theory, Maria Montero and co-authors first show that, theoretically, the issue with a higher value should get a disproportionally higher share of resources (that is, if one issue is worth twice as much as another, it should receive more than twice as many resources). They also show that players should “hedge” most of the time by spreading their resources widely. The theoretical distribution of resources is, however, rather complicated and involves probabilistic choices of allocations. In a laboratory experiment where subjects play this game repeatedly, the authors find that subjects whose strategy was less predictable were more successful than subjects who tended to play similar strategies twice in a row. When several games with different numbers of battlefields are compared, the authors find that subjects’ strategies were more sophisticated in the more difficult games. Over time, hedging strategies were played more often, though not as often as would be optimal. The most valuable issue was favoured over others but not as disproportionately as the theory predicts. Overall, in this complicated setting, the collective wisdom of the experiment participants, although not perfectly, approximated a complicated theoretical solution.
Forthcoming Economic Theory, “Majoritarian Blotto Contests with Asymmetric Battlefields: An Experiment on Apex Games”, by Maria Montero, Alex Possajennikov, Martin Sefton and Theodore L. Turocy
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Posted on Friday 2nd October 2015