Abstract
This research studied the strategies that players use in sequential adversarial games. We took the Rock-Paper-Scissors (RPS) game as an example and ran players in two experiments. The first experiment involved two humans, who played the RPS together for 100 times. Importantly, our payoff design in the RPS allowed us to differentiate between participants who used a random strategy from those who used a Nash strategy. We found that participants did not play in agreement with the Nash strategy, but rather, their behavior was closer to random. Moreover, the analyses of the participants’ sequential actions indicated heterogeneous cycle-based behaviors: some participants’ actions were independent of their past outcomes, some followed a well-known win-stay/lose-change strategy, and others exhibited the win-change/lose-stay behavior. To understand the sequential patterns of outcome-dependent actions, we designed probabilistic computer algorithms involving specific change actions (i.e., to downgrade or upgrade according to the immediate past outcome): the Win-Downgrade/Lose-Stay (WDLS) or Win-Stay/Lose-Upgrade (WSLU) strategies. Experiment 2 used these strategies against a human player. Our findings show that participants followed a win-stay strategy against the WDLS algorithm and a lose-change strategy against the WSLU algorithm, while they had difficulty in using an upgrade/downgrade direction, suggesting humans’ limited ability to detect and counter the actions of the algorithm. Taken together, our two experiments showed a large diversity of sequential strategies, where the win-stay/lose-change strategy did not describe the majority of human players’ dynamic behaviors in this adversarial situation.
Highlights
Almost everyone has settled disputes by playing a simple game called Rock-PaperScissors (RPS)
We first calculated the proportion of choices to investigate whether players’ behavior is in agreement with the Nash Equilibrium or the random strategy
We explored the serial dependency of actions, and focused on whether these actions were in agreement with the WSLC patterns
Summary
Almost everyone has settled disputes by playing a simple game called Rock-PaperScissors (RPS). Because rock can beat paper, but, at the same time, rock can be beaten by scissors, none of the selections (R, P, or S) is absolutely better than the other two This feature makes RPS a unique research paradigm to study sequential adversarial strategies in repeated interactions. Some research has focused on a frequency-based strategy (e.g., [4]), i.e., the (over)play of one selection (R, P, or S), while other research has focused on sequential actions based on memories of past actions and outcomes (cycle-based and outcome-based strategies). Players’ behavior might reveal sequential dependence patterns that are related to their contenders’ behavior
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