Measuring Level-K Reasoning, Satisficing, and Human Error in Game-Play Data

Abstract—Inferences about structured patterns in human de-cision making have been drawn from medium-scale simulated competitions with human subjects. The concepts analyzed in these studies include level-k thinking, satisficing, and other human error tendencies. These concepts can be mapped via a natural depth of search metric into the domain of chess, where copious data is available from hundreds of thousands of games by players of a wide range of precisely known skill levels in real competitions. The games are analyzed by strong chess programs to produce authoritative utility values for move decision options by progressive deepening of search. Our experiments show a significant relationship between the formulations of level-k thinking and the skill level of players. Notably, the players are distinguished solely on moves where they erred—according to the average depth level at which their errors are exposed by the authoritative analysis. Our results also indicate that the decisions are often independent of tail assumptions on higher-order beliefs. Further, we observe changes in this relationship in different contexts, such as minimal versus acute time pressure. We try to relate satisficing to insufficient level of reasoning and answer numerically the question, why do humans blunder? Key words. Game theory, level-k thinking, blunder, satisficing. I