Sequential Stackelberg Games with bounded rationality

doi:10.1016/j.asoc.2022.109846

2023-01-01

PRE

Jan Karwowski *

Jacek Mańdziuk

Adam Żychowski

DOI：10.1016/j.asoc.2022.109846

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Stackelberg Games (SGs) assume the perfect rationality of players. However, in real-life situations mod-eled by SGs, the followers may act not perfectly rationally, as their decisions may be affected/bounded by biases of various kinds, reflecting human behavior in the real world. Anchoring Theory (AT) is one of the popular bounded rationality (BR) models. It postulates that humans have a tendency to flatten the probabilities of the available options, i.e. their probability distribution is perceived as more uniform than is actually the case. This paper proposes a formulation of AT in sequential extensive-form SGs (ATSG) and its linearized approximate version (ATSGL) suitable for Mixed-Integer Linear Program (MILP) solution methods. ATSGL is implemented in three MILP/LP state-of-the-art methods for solving sequential SGs and compared with two recent non-MILP metaheuristic approaches based on the original non-simplified ATSG formulation, which rely on Monte Carlo sampling (O2UCT) and Evolutionary Algorithms (EASG), respectively. Experimental evaluation indicates that non-MILP heuristic approaches provide better solutions and scale better in time than MILPs in the AT setting. The efficacy of ATSG is further evaluated in experiments involving humans as followers, which show that it is more advantageous to use the ATSG leader's strategy than the Stackelberg Equilibrium strategy, which assumes the perfect rationality of the follower. The results confirm the existence of the human follower's AT-bias and the possibility to exploit it by the leader. An additional advantage of heuristic methods is the flexibility of the potential BR formulation they are able to incorporate.(c) 2022 Elsevier B.V. All rights reserved.

Keyword:

Sequential games

Stackelberg Games

Bounded rationality

Anchoring Theory

MILP