Heuristics for Strategy Choice: A Priority Heuristic for Games Patricia Rich Conference on Games, Interactive Rationality and Learning Lund 2012

Outline Goals of studying game situations How identifying heuristics for strategy choice will help to advance our goals A Priority Heuristic for some simple games New empirical evidence for the new heuristic Conclusions: the promise of heuristics for games, and future work

Four goals of studying games Mirror goals of studying non-strategic choice 2 descriptive, 1 normative, and 1 practical Different goals emphasized by different research agenda, but all are interconnected and considered important

Four goals Explaining strategic choices Many levels of explanation Individual cognitive processes the focus here Predicting choices

Four goals Evaluating strategic choices Normative judgments are valuable Prescriptions must be sensitive to reality Engineering to improve the world Better environments Better choice procedures Better outcomes

Heuristics can advance our goals Valuable knowledge from traditional economics and game theory Also some limitations: paradoxes, framing effects, off-equilibrium behavior... Bounded rationality offers some solutions Behavioral game theory and economics Heuristics improve on this

Heuristics can advance our goals Traditional and behavioral theories model people as optimizers ABC's fast and frugal heuristics program seeks true process models (heuristics) Success so far: e.g. recognition, priority, and take-the-best heuristics Natural to extend heuristics program to games (see also Leland, Hertwig and Fischbacher)

Heuristics for games Now, on to new work: first steps towards extending the heuristics program to strategic choice

Heuristics for games: some simple games Class of 2X2, PI, normal form games Such that column has a weakly dominant strategy, and row a unique best response Best response equilibrium offers maximum payoff to row, but other strategy offers a safe option with a good payoff First studied in extensive form by Beard and Beil, later by others

Heuristics for games: some simple games Almost no subjects use the same simple strategy for all games Strategy choice depends on many factors in a sophisticated way A heuristic explanation can account for all important choice factors, without assuming a complex choice procedure

Heuristics for games: some simple games 9, 4 D 3, 4.5 10, 5

Heuristics for games: some simple games x, y D z, q t, v

A new heuristic: roots The original priority heuristic Traditional decision criteria Behavioral insights

A new heuristic: the Priority Heuristic for games Step 1: Almost Certainty Step 2: Minimum Quality Step 3: Maximum Quality Step 4: If all else fails, randomize

Priority for games: an empirical test 100 users of Amazon's Mechanical Turk Told how to read game tables, with example Paid 1 cent per point earned Played 51 games, with sets of 5-6 each varying a factor of hypothesized importance No feedback during the experiment

An empirical test: the results Recall that D corresponds to best response, while U is safe Overall, 2 subjects always chose D, and 2 U Most striking result for games with punishment (column prefers U) 83% U, compared to 23-58 other series 7 subjects all-D non-pun, all-U pun

Step 1 factors: salience The presence of salience (0/1) is a significant predictor of response (0/1 for D/U) in a simple regression Regression coeff. -.057 p=.0027 Salience remains significant (p<.001) in a multiple regression with other important factors (with 4 minqual measures, pun, coeff. = -.096), with a relatively strong effect

Step 1 factors: column motivation 2 measures of col's motivation to obey dominance: q-v and q/v Surprisingly (based on a pilot), neither seems to be an important predictor of response Not significant in a simple regression Significant for aggregate #D and for response in multiple regression with some combinations of variables But overall, of little apparent importance

Step 1 factors: punishment 3 measures of punishment (col prefers U): Binary 0/1 Quotient y/v Difference y-v All significant in isolation, but multiple regression shows that the binary factor is what matters Even though only 6 of 51 games involve punishment, it has the second highest coefficient in a simple regression, p<.001

Step 1 overview Both salience and punishment, hypothesized step 1 factors, are indeed important. Punishment is by some standards the most important factor of them all: When present, causes extreme U choice Classification trees reliably pick it out as the first factor to use in dividing the data The clear importance of pun 0/1, in particular, suggests that subjects start by considering what their opponent is likely to do – just as the heuristic says

Step 2: minimum quality In the games studied, U's minimum is always of higher quality, often drastically so U's minqual, then, is measured by 4 factors: Quotients x/t and x/z Differences x-t and x-z So, the quality of the U payoff x depends on how it compares to the maximum (t) and D's minimum (z)

Step 2: minimum quality These factors are indeed highly important predictors of response: The classification algorithm picks out x/t < or >= .771, then x/z < or >= 2.688, then x/t >= or < .9625, in that order, as the biggest predictors of response, after pun, out of all the factors These values hint at the shape of the functions from payoff values to minqual to response

Step 2: minimum quality In the series set up to test aspects of minimum quality, more subjects choose U as its minqual increases, many switch from D to U as this happens, and most choice patterns are consistent with step 2 reasoning Consistent with the classification tree, this effect is strongest as x increases with respect to t, ceteris paribus

Step 2: minimum quality In simple regressions, x/t is by far the greatest predictor of response (coeff. about .86) and both x/t and x/z (.15) are far greater predictors than any individual payoff values or the difference measures of minqual In multiple regressions, these quotients consistently overshadow individual payoff variables, difference measures, etc. While x/t and x/z coeff's have p<.001 consistently, x and t themselves lose significance as predictors when quotients included

Step 2: overview The quality of U's minimum (guaranteed) payoff x is shown to be a major determining factor of subjects' responses As hypothesized, this quality is determined by x's relation to the maximum, t, and the alternative's (D's) minimum, with t being more important Subject behavior is consistent with step 2 reasoning

Step 3: maximum It was hypothesized that when minqual is not decisive, agents choose the strategy with the best max (D, here) In the games tested, this means that if step 2 is reached and U doesn't have a great min, D is chosen The data suggest that this is what happens: t-z is the only comparison relevant to max but not min The influence of t-z is negligable, while x compared to t is highly influential

An empirical test: summary These features of the data indicate that, firstly, the factors that would be important if subjects used the heuristic are indeed important The choice patterns are largely what one would expect given heuristic use The classification tree generated by a recursive partitioning algorithm provides a visual map of the most important parts of the heuristic procedure

An empirical test: alternative explanations Further, risk dominance with or without altruistic utility function does not explain the data A future experiment will be designed to more rigorously rule out altruism as a partial explanation Process data would be needed to prove conclusively that this particular heuristic is responsible for the data, but these results are encouraging

An empirical test: next steps Ruling out more alternative explanations It would be nice to have data on which payoffs people look at, for how long, in what order If the heuristic passes these tests, it should be generalized and analyzed from a normative perspective

Conclusions For the simple class of games presented here, the priority heuristic has the potential to explain strategic choices The heuristic is quite general already, and generalizing a bit further ought to enable it to handle a much wider class of games Step 1 is quite crucial, and how it is implemented may be the main difference between different classes of games

Conclusions The heuristic program for choice and inference has been progressing well, and is quite promising This new work shows that extending the program to games is within reach and will help us to achieve our 4 goals: explaining, predicting, evaulating, and engineering