Extensive form games with incentive stage-bidding: An emergence of non-cooperative cooperation

• 成果类型: Article
• 署名作者: Le Roux, Stephane; Goranko, Valentin
• 署名单位: Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Stockholm University; University of Witwatersrand
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2025.11.007
• 发表日期: 2026

摘要

This paper proposes and studies a mechanism modelling the emergence of cooperation in noncooperative multi-player extensive form games. We consider such games enriched with additional stage bidding actions, where at each decision node of the game tree, before the player controlling that node makes a decision every other player may make a committed offer ('bid') to pay an explicitly proposed amount of utility to the controlling player if she makes the choice explicitly indicated in the bid. In this work we assume that the bids are made simultaneously by all players. The controlling player then considers all these bids and then decides on its move. The effect of each bid associated with that choice is that it modifies the payoffs in the respective subgame according to the bid by transferring the proposed amounts of utility from the bidder to the controlling player who made the choice; all other bids made at that stage become irrelevant. Thus, these stage bids serve as an incentives-based mechanism that enables reaching a mutually beneficial cooperation in extensive form games. We study the resulting multi-player extensive form games with incentive bidding, which we call incentive bidding games (IB games), and analyze the subgame perfect equilibria (SPE) in these games. We show constructively that all IB games have (possibly many) SPE, and that the SPE outcomes (i.e. payoff tuples) form a polytope in the space of all outcomes. In the case of 2-player games, we also prove for an arbitrary game tree that all the SPE are sum-maximizing and have the same outcome, thereby defining a unique value of the game. These results contrast some well-known drawbacks of SPE in standard extensive form games and provide a further strong motivation for studying extensive form games with incentive bidding. We also study the notion of strong SPE in the sense of Aumann for IB games. First, we show that each of these strong SPE maximizes the sum of the payoffs (thus achieving a socially optimal solution). Second, if the game tree is binary, the strong SPE outcomes form a convex polytope. Third, games with only two leaves have such strong SPE, and we conjecture that all games with binary decision trees and with the same controlling player at all decision nodes have, indeed, such strong SPE.