Optimal strategies for symmetric matrix games with partitions
 Author
 Bart De Schuymer, Hans De Meyer (UGent) and Bernard De Baets (UGent)
 Organization
 Abstract
 We introduce three variants of a symmetric matrix game corresponding to three ways of comparing two partitions of a fixed integer (sigma) into a fixed number (n) of parts, In the random variable interpretation of the game, each variant depends on the choice of a copula that binds the marginal uniform cumulative distribution functions (cdf) into the bivariate cdf. The three copulas considered are the product copula TP and the two extreme copulas, i.e. the minimum Copula TM and the Lukasiewicz copula TL. The associated games are denoted as the (n, sigma)(P), (n, sigma)(M)and (n, sigma)(L) games. In the present paper, we characterize the optimal strategies of the (n, sigma)(M) and (n, sigma)(L) games and compare them to the optimal strategies of the (n, sigma)(P) games. It turns out that the characterization of the optimal strategies is completely different for each game variant.
 Keywords
 Partition theory, Optimal strategy, Matrix game, Probabilistic relation, Copula
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU693922
 MLA
 De Schuymer, Bart, Hans De Meyer, and Bernard De Baets. “Optimal Strategies for Symmetric Matrix Games with Partitions.” BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETYSIMON STEVIN 16.1 (2009): 67–89. Print.
 APA
 De Schuymer, B., De Meyer, H., & De Baets, B. (2009). Optimal strategies for symmetric matrix games with partitions. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETYSIMON STEVIN, 16(1), 67–89.
 Chicago authordate
 De Schuymer, Bart, Hans De Meyer, and Bernard De Baets. 2009. “Optimal Strategies for Symmetric Matrix Games with Partitions.” Bulletin of the Belgian Mathematical Societysimon Stevin 16 (1): 67–89.
 Chicago authordate (all authors)
 De Schuymer, Bart, Hans De Meyer, and Bernard De Baets. 2009. “Optimal Strategies for Symmetric Matrix Games with Partitions.” Bulletin of the Belgian Mathematical Societysimon Stevin 16 (1): 67–89.
 Vancouver
 1.De Schuymer B, De Meyer H, De Baets B. Optimal strategies for symmetric matrix games with partitions. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETYSIMON STEVIN. 2009;16(1):67–89.
 IEEE
 [1]B. De Schuymer, H. De Meyer, and B. De Baets, “Optimal strategies for symmetric matrix games with partitions,” BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETYSIMON STEVIN, vol. 16, no. 1, pp. 67–89, 2009.
@article{693922, abstract = {We introduce three variants of a symmetric matrix game corresponding to three ways of comparing two partitions of a fixed integer (sigma) into a fixed number (n) of parts, In the random variable interpretation of the game, each variant depends on the choice of a copula that binds the marginal uniform cumulative distribution functions (cdf) into the bivariate cdf. The three copulas considered are the product copula TP and the two extreme copulas, i.e. the minimum Copula TM and the Lukasiewicz copula TL. The associated games are denoted as the (n, sigma)(P), (n, sigma)(M)and (n, sigma)(L) games. In the present paper, we characterize the optimal strategies of the (n, sigma)(M) and (n, sigma)(L) games and compare them to the optimal strategies of the (n, sigma)(P) games. It turns out that the characterization of the optimal strategies is completely different for each game variant.}, author = {De Schuymer, Bart and De Meyer, Hans and De Baets, Bernard}, issn = {13701444}, journal = {BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETYSIMON STEVIN}, keywords = {Partition theory,Optimal strategy,Matrix game,Probabilistic relation,Copula}, language = {eng}, number = {1}, pages = {6789}, title = {Optimal strategies for symmetric matrix games with partitions}, volume = {16}, year = {2009}, }