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

2. 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

3. 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

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

5. 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

6. 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

7. 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)

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

9. 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

10. 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

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

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

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

14. 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

15. 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

16. 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 other series
7 subjects all-D non-pun, all-U pun

17. 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
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

18. 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

19. 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

20. 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

21. 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)

22. 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 < , 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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