### Abstract

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.

Original language | English (US) |
---|---|

Article number | 5585787 |

Pages (from-to) | 341-349 |

Number of pages | 9 |

Journal | IEEE Transactions on Systems, Man, and Cybernetics: Systems |

Volume | 41 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2011 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software
- Control and Systems Engineering
- Human-Computer Interaction
- Computer Science Applications
- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Systems, Man, and Cybernetics: Systems*,

*41*(2), 341-349. [5585787]. https://doi.org/10.1109/TSMCA.2010.2064302

}

*IEEE Transactions on Systems, Man, and Cybernetics: Systems*, vol. 41, no. 2, 5585787, pp. 341-349. https://doi.org/10.1109/TSMCA.2010.2064302

**On bandwidth-limited sum-of-games problems.** / Dingankar, C.; Karandikar, Sampada; Brooks, R.; Griffin, Christopher.

Research output: Contribution to journal › Article

TY - JOUR

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

AU - Dingankar, C.

AU - Karandikar, Sampada

AU - Brooks, R.

AU - Griffin, Christopher

PY - 2011/3/1

Y1 - 2011/3/1

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 -