1. Implicit Centipedes (joint with Daniil Starikov and Gleb Vasiliev)
The centipede game illustrates a strategic interaction in which real-world players often deviate from the subgame perfect Nash equilibrium. In previous laboratory experiments, participants typically observed the full game tree, including payoff structures. Even under these relatively simple conditions, cognitive capacity has been linked to adherence to the equilibrium path. However, the explicit presentation of the game may significantly influence this outcome. Consider instead a more complex, implicitly defined problem that effectively constitutes a centipede game. In such cases, more advanced players may perform better by inferring the underlying structure of the game. Conversely, if the game is too complex to be solved — even by highly skilled players — then the resulting interaction may diverge significantly from equilibrium predictions, leading to unpredictable outcomes. To explore the dynamics of implicitly formulated games, we examine an antagonistic variant of the centipede game played by professional athletes—specifically, Formula 1 drivers and their teams—during races. When two drivers are in close proximity, they engage in a strategic contest with the goal of finishing ahead of one another. Each lap presents a decision point: the leading driver and the pursuer sequentially decide whether to pit and change tires. Analyzing intra-race data from multiple Formula 1 seasons, we demonstrate that this scenario constitutes a complex, centipede-like game. Although the drivers do not observe the explicit game tree, our findings reveal that more skilled drivers and teams adopt strategies that more closely align with theoretical equilibrium predictions, despite the game's implicit nature.
2. Antagonistic sequential games with ties between players with limited search capacity
I consider an important class of antagonistic sequential games of value 0 with ties, where players do not have enough memory capacity to solve the game using backward induction. Checkers and supposedly chess belong to this class. In such games the level of human players is associated with the number and severity of mistakes (deviations from the subgame perfect equilibrium). One of the most popular ways to predict an outcome of such games is based on the paired comparison model. I show formally that for this class of games a predictive model that matches the empirical evidence, cannot be obtained in a paired comparison framework: two types of the desirable monotonicity lead to incompatibility. A relaxation of monotonicity properties that allows a solution to be found is also proposed in the paper.
The centipede game illustrates a strategic interaction in which real-world players often deviate from the subgame perfect Nash equilibrium. In previous laboratory experiments, participants typically observed the full game tree, including payoff structures. Even under these relatively simple conditions, cognitive capacity has been linked to adherence to the equilibrium path. However, the explicit presentation of the game may significantly influence this outcome. Consider instead a more complex, implicitly defined problem that effectively constitutes a centipede game. In such cases, more advanced players may perform better by inferring the underlying structure of the game. Conversely, if the game is too complex to be solved — even by highly skilled players — then the resulting interaction may diverge significantly from equilibrium predictions, leading to unpredictable outcomes. To explore the dynamics of implicitly formulated games, we examine an antagonistic variant of the centipede game played by professional athletes—specifically, Formula 1 drivers and their teams—during races. When two drivers are in close proximity, they engage in a strategic contest with the goal of finishing ahead of one another. Each lap presents a decision point: the leading driver and the pursuer sequentially decide whether to pit and change tires. Analyzing intra-race data from multiple Formula 1 seasons, we demonstrate that this scenario constitutes a complex, centipede-like game. Although the drivers do not observe the explicit game tree, our findings reveal that more skilled drivers and teams adopt strategies that more closely align with theoretical equilibrium predictions, despite the game's implicit nature.
2. Antagonistic sequential games with ties between players with limited search capacity
I consider an important class of antagonistic sequential games of value 0 with ties, where players do not have enough memory capacity to solve the game using backward induction. Checkers and supposedly chess belong to this class. In such games the level of human players is associated with the number and severity of mistakes (deviations from the subgame perfect equilibrium). One of the most popular ways to predict an outcome of such games is based on the paired comparison model. I show formally that for this class of games a predictive model that matches the empirical evidence, cannot be obtained in a paired comparison framework: two types of the desirable monotonicity lead to incompatibility. A relaxation of monotonicity properties that allows a solution to be found is also proposed in the paper.
Economics, Game Theory, Computer Science, Sports Studies
Dmitry Dagaev
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