Robust optimization with applications to game theory. (English) Zbl 1175.90375
Summary: We investigate robust optimization equilibria with two players, in which each player can neither evaluate his opponent’s strategy nor his own cost matrix accurately while may estimate a bounded set of the strategy or cost matrix. We obtain a result that solving this equilibria can be formulated as solving a second-order cone complementarity problem under an ellipsoid uncertainty set or a mixed complementarity problem under a box uncertainty set. We present some numerical results to illustrate the behaviour of robust optimization equilibria.
Keywords:
robust optimization equilibria; bimatrix game; strategy uncertainty; cost matrix uncertainty; second-order cone complementarity problem; mixed complementarity problemReferences:
| [1] | DOI: 10.1073/pnas.36.1.48 · Zbl 0036.01104 · doi:10.1073/pnas.36.1.48 |
| [2] | DOI: 10.2307/1969529 · Zbl 0045.08202 · doi:10.2307/1969529 |
| [3] | DOI: 10.1287/mnsc.14.3.159 · Zbl 0207.51102 · doi:10.1287/mnsc.14.3.159 |
| [4] | DOI: 10.1007/s10287-004-0010-0 · Zbl 1115.90059 · doi:10.1007/s10287-004-0010-0 |
| [5] | DOI: 10.1016/j.orl.2006.03.004 · Zbl 1303.91020 · doi:10.1016/j.orl.2006.03.004 |
| [6] | DOI: 10.1007/s10107-007-0160-2 · Zbl 1166.90015 · doi:10.1007/s10107-007-0160-2 |
| [7] | DOI: 10.1007/s10107-005-0686-0 · Zbl 1134.91309 · doi:10.1007/s10107-005-0686-0 |
| [8] | DOI: 10.1016/S0167-6377(99)00016-4 · Zbl 0941.90053 · doi:10.1016/S0167-6377(99)00016-4 |
| [9] | DOI: 10.1007/PL00011380 · doi:10.1007/PL00011380 |
| [10] | DOI: 10.1007/s10107-006-0092-2 · Zbl 1135.90046 · doi:10.1007/s10107-006-0092-2 |
| [11] | DOI: 10.1016/j.orl.2003.12.007 · Zbl 1054.90046 · doi:10.1016/j.orl.2003.12.007 |
| [12] | Facchinei F, Finite-dimensional Variational Inequalities and Complementarity Problems (2003) · Zbl 1062.90002 |
| [13] | DOI: 10.1023/A:1022996819381 · Zbl 1038.90084 · doi:10.1023/A:1022996819381 |
| [14] | DOI: 10.1137/S1052623400380365 · Zbl 0995.90094 · doi:10.1137/S1052623400380365 |
| [15] | DOI: 10.1287/moor.1040.0120 · Zbl 1082.90151 · doi:10.1287/moor.1040.0120 |
| [16] | DOI: 10.1016/S0024-3795(98)10032-0 · Zbl 0946.90050 · doi:10.1016/S0024-3795(98)10032-0 |
| [17] | DOI: 10.1007/s10107-005-0677-1 · Zbl 1134.90026 · doi:10.1007/s10107-005-0677-1 |
| [18] | Hayashi S, J. Nonlinear Convex Anal. 6 pp 283– (2005) |
| [19] | DOI: 10.1137/S1052623403421516 · Zbl 1114.90139 · doi:10.1137/S1052623403421516 |
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