Synthesis problems on multiplayer non-zero-sum games (MG) with multiple environment players that behave rationally are the problems to find a good strategy of the system and have been extensively studied. This paper concerns the synthesis problems on stochastic MG (SMG), where a special controller other than players, called nature, which chooses a move in its turn randomly, may exist. Two types of synthesis problems on SMG exist: cooperative rational synthesis problem (CRSP) and non-cooperative rational synthesis problem (NCRSP). The rationality of environment players is modeled by Nash equilibria, and CRSP is the problem to decide whether there exists a Nash equilibrium that gives the system a payoff not less than a given threshold. Ummels et al. studied the complexity of CRSP for various classes of objectives and strategies of players. CRSP fits the situation where the system can make a suggestion of a strategy profile (a tuple of strategies of all players) to the environment players. However, in real applications, the system may rarely have an opportunity to make suggestions to the environment, and thus CRSP is optimistic. NCRSP is the problem to decide whether there exists a strategy σ0 of the system satisfying that for every strategy profile of the environment players that forms a 0-fixed Nash equilibrium (a Nash equilibrium where the system's strategy is fixed to σ0), the system obtains a payoff not less than a given threshold. In this paper, we investigate the complexity of NCRSP for positional (i.e. pure memoryless) strategies. We consider ω-regular objectives as the model of players' objectives, and show the complexity results of the problem for several subclasses of ω-regular objectives. In particular, the problem for terminal reachability (TR) objectives is shown to be Σp2-complete.
So KOIDE
Nagoya University
Yoshiaki TAKATA
Kochi University of Technology
Hiroyuki SEKI
Nagoya University
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So KOIDE, Yoshiaki TAKATA, Hiroyuki SEKI, "Non-Cooperative Rational Synthesis Problem on Stochastic Games for Positional Strategies" in IEICE TRANSACTIONS on Information,
vol. E107-D, no. 3, pp. 301-311, March 2024, doi: 10.1587/transinf.2023FCP0003.
Abstract: Synthesis problems on multiplayer non-zero-sum games (MG) with multiple environment players that behave rationally are the problems to find a good strategy of the system and have been extensively studied. This paper concerns the synthesis problems on stochastic MG (SMG), where a special controller other than players, called nature, which chooses a move in its turn randomly, may exist. Two types of synthesis problems on SMG exist: cooperative rational synthesis problem (CRSP) and non-cooperative rational synthesis problem (NCRSP). The rationality of environment players is modeled by Nash equilibria, and CRSP is the problem to decide whether there exists a Nash equilibrium that gives the system a payoff not less than a given threshold. Ummels et al. studied the complexity of CRSP for various classes of objectives and strategies of players. CRSP fits the situation where the system can make a suggestion of a strategy profile (a tuple of strategies of all players) to the environment players. However, in real applications, the system may rarely have an opportunity to make suggestions to the environment, and thus CRSP is optimistic. NCRSP is the problem to decide whether there exists a strategy σ0 of the system satisfying that for every strategy profile of the environment players that forms a 0-fixed Nash equilibrium (a Nash equilibrium where the system's strategy is fixed to σ0), the system obtains a payoff not less than a given threshold. In this paper, we investigate the complexity of NCRSP for positional (i.e. pure memoryless) strategies. We consider ω-regular objectives as the model of players' objectives, and show the complexity results of the problem for several subclasses of ω-regular objectives. In particular, the problem for terminal reachability (TR) objectives is shown to be Σp2-complete.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2023FCP0003/_p
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@ARTICLE{e107-d_3_301,
author={So KOIDE, Yoshiaki TAKATA, Hiroyuki SEKI, },
journal={IEICE TRANSACTIONS on Information},
title={Non-Cooperative Rational Synthesis Problem on Stochastic Games for Positional Strategies},
year={2024},
volume={E107-D},
number={3},
pages={301-311},
abstract={Synthesis problems on multiplayer non-zero-sum games (MG) with multiple environment players that behave rationally are the problems to find a good strategy of the system and have been extensively studied. This paper concerns the synthesis problems on stochastic MG (SMG), where a special controller other than players, called nature, which chooses a move in its turn randomly, may exist. Two types of synthesis problems on SMG exist: cooperative rational synthesis problem (CRSP) and non-cooperative rational synthesis problem (NCRSP). The rationality of environment players is modeled by Nash equilibria, and CRSP is the problem to decide whether there exists a Nash equilibrium that gives the system a payoff not less than a given threshold. Ummels et al. studied the complexity of CRSP for various classes of objectives and strategies of players. CRSP fits the situation where the system can make a suggestion of a strategy profile (a tuple of strategies of all players) to the environment players. However, in real applications, the system may rarely have an opportunity to make suggestions to the environment, and thus CRSP is optimistic. NCRSP is the problem to decide whether there exists a strategy σ0 of the system satisfying that for every strategy profile of the environment players that forms a 0-fixed Nash equilibrium (a Nash equilibrium where the system's strategy is fixed to σ0), the system obtains a payoff not less than a given threshold. In this paper, we investigate the complexity of NCRSP for positional (i.e. pure memoryless) strategies. We consider ω-regular objectives as the model of players' objectives, and show the complexity results of the problem for several subclasses of ω-regular objectives. In particular, the problem for terminal reachability (TR) objectives is shown to be Σp2-complete.},
keywords={},
doi={10.1587/transinf.2023FCP0003},
ISSN={1745-1361},
month={March},}
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TY - JOUR
TI - Non-Cooperative Rational Synthesis Problem on Stochastic Games for Positional Strategies
T2 - IEICE TRANSACTIONS on Information
SP - 301
EP - 311
AU - So KOIDE
AU - Yoshiaki TAKATA
AU - Hiroyuki SEKI
PY - 2024
DO - 10.1587/transinf.2023FCP0003
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E107-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 2024
AB - Synthesis problems on multiplayer non-zero-sum games (MG) with multiple environment players that behave rationally are the problems to find a good strategy of the system and have been extensively studied. This paper concerns the synthesis problems on stochastic MG (SMG), where a special controller other than players, called nature, which chooses a move in its turn randomly, may exist. Two types of synthesis problems on SMG exist: cooperative rational synthesis problem (CRSP) and non-cooperative rational synthesis problem (NCRSP). The rationality of environment players is modeled by Nash equilibria, and CRSP is the problem to decide whether there exists a Nash equilibrium that gives the system a payoff not less than a given threshold. Ummels et al. studied the complexity of CRSP for various classes of objectives and strategies of players. CRSP fits the situation where the system can make a suggestion of a strategy profile (a tuple of strategies of all players) to the environment players. However, in real applications, the system may rarely have an opportunity to make suggestions to the environment, and thus CRSP is optimistic. NCRSP is the problem to decide whether there exists a strategy σ0 of the system satisfying that for every strategy profile of the environment players that forms a 0-fixed Nash equilibrium (a Nash equilibrium where the system's strategy is fixed to σ0), the system obtains a payoff not less than a given threshold. In this paper, we investigate the complexity of NCRSP for positional (i.e. pure memoryless) strategies. We consider ω-regular objectives as the model of players' objectives, and show the complexity results of the problem for several subclasses of ω-regular objectives. In particular, the problem for terminal reachability (TR) objectives is shown to be Σp2-complete.
ER -