The Role of Precedence in Coordination Games: A Study on Strategic Decision-Making

Abstract

This study investigates how precedence, defined as the joint history of past interactions, shapes strategic decision-making in coordination games.

Previous work has shown that, in coordination problems, repeated play allows participants to form conventions by maintaining strategies that proved successful [1], [2]. We ask whether the same mechanism operates when success requires selecting complementary (rather than identical) items, and whether participants can abstract a coordination pattern during practice that transfers to novel stimuli.

In earlier studies, when players had to coordinate by choosing the same option (e.g., the same color), repeated play established a focal “Schelling point” that boosted coordination above chance [1], [3]. We extend this paradigm to complementary coordination problems: in each round, a dyad wins only if players’ pieces interlock to form a target shape. Players choose simultaneously, without communication, but can see each other's available options. Pieces vary in size and orientation, and coordination may also require establishing complementary roles, that is, deciding who selects which type of piece. Each test round presents two strategically valid solutions, both representing Nash equilibria, based either on physical features or on role assignment.

The study includes two conditions. In the baseline condition, participants play single, one-shot test rounds without prior interaction or feedback. Since each configuration allows two different interlocking combinations, with no clear reason to prefer one over the other, the rounds are inherently ambiguous, and coordination does not differ significantly from chance. In the joint-history condition, applied to new dyads, each test round (identical to those in the baseline) is preceded by three guided practice rounds with the same partner, using different figures. These rounds guide players toward one specific strategy, with immediate feedback after each choice. Successful coordination in the test rounds, significantly above chance, indicates transfer of the practiced strategy to novel cases, establishing it as the focal pattern.

We predict that coordination rates in the joint-history condition will be significantly higher than in the baseline, due to the prior guided interaction. This would demonstrate that joint history can create a strategy-specific Schelling salience, making the practiced pattern the natural point of convergence even in novel contexts. To assess whether coordination rates within each condition differ from chance (50%), we will use binomial tests. Additionally, to compare coordination rates directly between the two conditions, we will apply chi-square tests in R.

By showing that experimenter-guided history rounds induce transferable abstract patterns in complementary coordination, we clarify how conventions emerge through precedence. Our findings aim to clarify the cognitive processes by which people form and apply coordination strategies without verbal communication.

References

[1] L. Voronina et al., “Joint history of play provides means for coordination,” in Proc. Information Society 2022, Ljubljana, Slovenia, Oct. 2022.

[2] M. Knez and C. Camerer, “Increasing cooperation in prisoner's dilemmas by establishing a precedent of efficiency in coordination games,” Organ. Behav. Hum. Decis. Process., vol. 82, no. 2, pp. 194–216, Jul. 2000.

[3] T. C. Schelling, The Strategy of Conflict, 1^st ed., Cambridge, MA: Harvard University Press, 1960.