6 papers
Equilibrium Numbers in Non-Square Bimatrix Games
Constantin Ickstadt, Thorsten Theobald, Bernhard von Stengel
Bimatrix games may have an exponential number of mixed Nash equilibria if both dimensions of the game are allowed to grow. Bounds on their maximal number give structural insights t…
On the equivalence of semidefinite programming and zero-sum semidefinite games
Jesse Elliott, Constantin Ickstadt, Thorsten Theobald +1
By results of Dantzig (1951) and Adler (2013), computing the optimal solutions of a linear program is equivalent to finding optimal strategies in zero-sum bimatrix games. Dantzig's…
Nash equilibria in semidefinite games and Lemke-Howson paths
Constantin Ickstadt, Thorsten Theobald, Elias Tsigaridas +1
We consider an algorithmic framework for two-player non-zero-sum semidefinite games, where each player's strategy is a positive semidefinite matrix with trace one. We formulate the…
A Stable-Set Bound and Maximal Numbers of Nash Equilibria in Bimatrix Games
Constantin Ickstadt, Thorsten Theobald, Bernhard von Stengel
Quint and Shubik (1997) conjectured that a non-degenerate n-by-n game has at most 2^n-1 Nash equilibria in mixed strategies. The conjecture is true for n at most 4 but false for n=…
Semidefinite network games: multiplayer minimax and complementarity problems
Constantin Ickstadt, Thorsten Theobald, Elias Tsigaridas +1
Network games provide a powerful framework for modeling agent interactions in networked systems, where players are represented by nodes in a graph and their payoffs depend on the a…
Semidefinite games
Constantin Ickstadt, Thorsten Theobald, Elias Tsigaridas
We introduce and study the class of semidefinite games, which generalizes bimatrix games and finite -person games, by replacing the simplex of the mixed strategies for each play…