TY - JOUR

T1 - On bandwidth-limited sum-of-games problems

AU - Dingankar, C.

AU - Karandikar, Sampada

AU - Brooks, R.

AU - Griffin, C.

N1 - Funding Information:
The works of R. Brooks and C. Dingankar were supported in part by the U.S. Army Research Laboratory and in part by the U.S. Army Research Office under Grant W911NF-05-10226 (Adaptive and Cooperative Autonomous Systems). The works of R. Brooks and C. Griffin were supported in part by the Office of Naval Research under Grant N00014-06-0022 (Learning and Prediction for Enhanced Readiness). The work of R. Brooks was supported in part by the Air Force Office of Scientific Research under Grant FA9550-09-1-0173. The opinions expressed here are those of the author and not the U.S. Department of Defense
Funding Information:
Manuscript received June 17, 2009; revised December 22, 2009; accepted April 22, 2010. Date of publication September 27, 2010; date of current version January 19, 2011. The works of R. Brooks and C. Dingankar were supported in part by the U.S. Army Research Laboratory and in part by the U.S. Army Research Office under Grant W911NF-05-10226 (Adaptive and Cooperative Autonomous Systems). The works of R. Brooks and C. Griffin were supported in part by the Office of Naval Research under Grant N00014-06-0022 (Learning and Prediction for Enhanced Readiness). The work of R. Brooks was supported in part by the Air Force Office of Scientific Research under Grant FA9550-09-1-0173. The opinions expressed here are those of the author and not the U.S. Department of Defense. This paper was recommended by Associate Editor S. Mori.
Publisher Copyright:
© 2010 IEEE.

PY - 2011/3

Y1 - 2011/3

N2 - Game theory typically considers two types of imperfect information when analyzing conflicts: 1) chance moves and 2) information sets. This correspondence paper considers games where players compete on many fronts without having sufficient bandwidth to collect the game trees describing all the conflicts. The player therefore needs to prioritize between subgames without having detailed information about the subgames. We address this problem by using two combinatorial game theory tools: 1) surreal numbers and 2) thermographs. We consider the global conflict as a sum-of-games problem, which is known to be intractable (PSPACE complete). Known combinatorial game theory heuristics can analyze surreal-number encodings of games using thermographs to find solutions that are within a known constant offset of the optimal solution. To apply the combinatorial game theory to this domain, we first integrate chance moves into surreal-number encodings of games by showing that the expected values of surreal numbers are surreal numbers. We then show that, of the three commonly used sum-of-games heuristics, only hotstrat is applicable to this domain. Simulations compare solutions found using hotstrat to solution approaches used by other researchers on a similar problem (maximin, maximax, and mean). The simulations show that the hotstrat solutions dominate the existing approaches.

AB - Game theory typically considers two types of imperfect information when analyzing conflicts: 1) chance moves and 2) information sets. This correspondence paper considers games where players compete on many fronts without having sufficient bandwidth to collect the game trees describing all the conflicts. The player therefore needs to prioritize between subgames without having detailed information about the subgames. We address this problem by using two combinatorial game theory tools: 1) surreal numbers and 2) thermographs. We consider the global conflict as a sum-of-games problem, which is known to be intractable (PSPACE complete). Known combinatorial game theory heuristics can analyze surreal-number encodings of games using thermographs to find solutions that are within a known constant offset of the optimal solution. To apply the combinatorial game theory to this domain, we first integrate chance moves into surreal-number encodings of games by showing that the expected values of surreal numbers are surreal numbers. We then show that, of the three commonly used sum-of-games heuristics, only hotstrat is applicable to this domain. Simulations compare solutions found using hotstrat to solution approaches used by other researchers on a similar problem (maximin, maximax, and mean). The simulations show that the hotstrat solutions dominate the existing approaches.

UR - http://www.scopus.com/inward/record.url?scp=85028276713&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028276713&partnerID=8YFLogxK

U2 - 10.1109/TSMCA.2010.2064302

DO - 10.1109/TSMCA.2010.2064302

M3 - Article

AN - SCOPUS:85028276713

VL - 41

SP - 341

EP - 349

JO - IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans

JF - IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans

SN - 1083-4427

IS - 2

M1 - 5585787

ER -