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Spiliopoulous, L. & Hertwig, R. (2019). Strategic uncertainty and incomplete information: Homo heuristicus does not fold. In R. Hertwig, T. Pleskac, T. Pachur, & the Center for Adaptive Rationality (Eds.), Taming uncertainty (pp. xx–xx). Boston, MA: MIT Press. doi:XXXXXXX

Chapter 5 Heuristics, Strategic Uncertainty, and Incomplete Information

Introduction

The performance of decision policies is dependent not only on environmental characteristics such as game size and degree of payoff uncertainty, but also on the concentration of opponent policies in the population. In this element, you can examine this by defining the frequency of occurrence of decision policies in the population. Each heatmap presents the performance of a specific decision policy against the population you have specified, for variations in the game size and degree of missing payoff information.

The size of the actions space (or game) is the number of actions each players has at their disposal. The % of missing payoffs indicates the likelihood that each piece of payoff information of the game is unknown to the player.

We recommended that you explore the effects of a population comprised mostly of complex decision policies based on strategic considerations, such as the Nash equilibrium, Level-2, or Level-3, versus a population of simple decision policies such as Maxmax, Maxmin, Equality or Social maximum.

Note: The letter "M" will appear in the subplot of the specific decision policy that achieves the highest possible performance for each combination of game size and % of missing payoffs.

Decision rule Description % Distribution
Random Chooses the action(s) randomly
Maxmax Chooses the action(s) offering the highest payoff for the player
Maxmin Chooses the action(s) offering the highest worst-case payoff for the player
Social maximum Chooses the action(s) maximizing the sum of the player’s own payoff and the opponent’s payoff
Equality Chooses the action(s) minimizing the difference between the player’s own payoff and the opponent’s payoff
Dominance-1 Chooses the action(s) offering the best response to the assumption that an opponent is choosing randomly over their nondominated actions
Level-1 Chooses the action(s) offering the best response to the assumption that an opponent is choosing randomly
Level-2 Chooses the action(s) offering the best response to the assumption that an opponent is applying L1
Level-3 Chooses the action(s) offering the best response to the assumption that an opponent is applying L2
Nash equilibrium Chooses the action(s) consistent with the pure strategy Nash equilibrium (with the highest joint payoffs)
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In strategic decision-making, the performance of decision policies depends not only on their interaction with the environment (such as the types of games played, the degree of conflict generated by said games, missing payoff information etc), but also on the distribution of the opponent decision policies in the population. By varying this distribution using this tool, you investigated the robustness of decision policies to strategic uncertainty. In particular, the L1 and D1 heuristics remain highly competitive for a wide range of possible distributions of opponents. By contrast, decision policies that make specific assumptions about their opponent, such as the Nash equilibrium and MaxMax, performed well only when these assumptions matched the characteristics of the majority of opponents. Otherwise, they performed relatively poorly, that is, they were not robust to strategic uncertainty.

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