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Economics
Game Theory

Strategic Negotiations for Extensive-Form Games

Profile image of Dave de JongeDave de Jonge

2020, Autonomous Agents and Multi-Agent Systems

https://doi.org/10.1007/S10458-019-09424-Y
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45 pages

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Abstract

When studying extensive-form games it is commonly assumed that players make their decisions individually. One usually does not allow the possibility for the players to negotiate their respective strategies and formally commit themselves to future moves. As a consequence, many non-zero-sum games have been shown to have equilibrium outcomes that are suboptimal and arguably counter-intuitive. For this reason we feel there is a need to explore a new line of research in which game-playing agents are allowed to negotiate binding agreements before they make their moves. We analyze what happens under such assumptions and define a new equilibrium solution concept to capture this. We show that this new solution concept indeed yields solutions that are more efficient and, in a sense, closer to what one would expect in the real world. Furthermore, we demonstrate that our ideas are not only theoretical in nature , but can also be implemented on bounded rational agents, with a number of experiments conducted with a new algorithm that combines techniques from Automated Negotiations, (Algorithmic) Game Theory, and General Game Playing. Our algorithm, which we call Monte Carlo Negotiation Search, is an adaptation of Monte Carlo Tree Search that equips the agent with the ability to negotiate. It is completely domain-independent in the sense that it is not tailored to any specific game. It can be applied to any non-zero-sum game, provided that its rules are described in Game Description Language. We show with several experiments that it strongly outperforms non-negotiating players, and that it closely approximates the theoretically optimal outcomes, as defined by our new solution concept.

Figures (4)
Fig. 1 State space of the Centipede Game. Next to each terminal state tz, on the right-hand side, we have indicated its utility vector. Next to each non-terminal state wz, on the left-hand side, we have indicated its Negotiation Values nv,,7,; and Reservation Values ru, 7; (Sec. 6.3), assuming no deal has been made in any earlier round.
Fig. 1 State space of the Centipede Game. Next to each terminal state tz, on the right-hand side, we have indicated its utility vector. Next to each non-terminal state wz, on the left-hand side, we have indicated its Negotiation Values nv,,7,; and Reservation Values ru, 7; (Sec. 6.3), assuming no deal has been made in any earlier round.
Strategic Negotiations for Extensive-Form Games
Strategic Negotiations for Extensive-Form Games
Fig. 2 The Iterated Prisoner’s Dilemma, with varying number of rounds per match. The value on the vertical axis is the utility averaged over 50 matches and over the two agents. Table 1 Without negotiations the results are exactly the Subgame Perfect Equilibrium values. With negotiations the results clearly dominate the results without negotiations and are close to optimal.
Fig. 2 The Iterated Prisoner’s Dilemma, with varying number of rounds per match. The value on the vertical axis is the utility averaged over 50 matches and over the two agents. Table 1 Without negotiations the results are exactly the Subgame Perfect Equilibrium values. With negotiations the results clearly dominate the results without negotiations and are close to optimal.
Fig. 3 State space of the Dollar Auction. Next to each terminal state t;,, on the right-hand side, we have indicated its utility vector. Next to each non-terminal state wz, on the left- hand side, we have indicated its Subgame Perfect Equilibrium values spe,, 7, assuming no agreements have been made. Also, on the left-hand side next to the arrows we have indicated the active player. The thick arrows indicate the optimal moves.
Fig. 3 State space of the Dollar Auction. Next to each terminal state t;,, on the right-hand side, we have indicated its utility vector. Next to each non-terminal state wz, on the left- hand side, we have indicated its Subgame Perfect Equilibrium values spe,, 7, assuming no agreements have been made. Also, on the left-hand side next to the arrows we have indicated the active player. The thick arrows indicate the optimal moves.

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