Is It Worth Surprising Your Prospective Employer?

In game theoretic jargon, "forward induction" is a kind of strategic reasoning. When player A (Ann) sees a move by player B (Bob), she asks herself: "How is Bob going to continue his play?" and "What does Bob know that I don't?" The reaction of Ann depends on how she answers these questions. The answer is predetermined by Ann's original beliefs if the observed move was to some extent expected, i.e. if she initially assigned positive probability to this move. In this case she just has to apply the rules of conditional probabilities (Bayes rule) and we are back to an analysis of how Ann initially predicts the behavior of Bob. But such rules have no bite if Bob's move is unexpected. According to the forward induction principle, Ann rationalizes Bob's move, that is, she assumes that Bob is playing what he thinks to be his best strategy.

Modeling reactions to unexpected moves, and predictions about such reactions, is the bread and butter of game theory. Indeed, a player's prediction about his co-player reaction to an unexpected move is what determines his incentives to surprise the other player in the first place. Suppose nobody (in a given community) is studying a difficult subject that is much harder to learn for low-talent students. Does it pay off for a high-talent student to surprise potential employers and study this subject? If the employers' inference is "This must be a high-talent type who is trying to get a high-pay job", then studying the hard subject is probably worth the effort. But if we are in a very conformist society where it is commonly assumed that it does not pay off to behave differently from other people, then the choice of studying the hard subject cannot be rationalized and it will look suspicious to potential employers. Indeed, they may think "Nobody in his right mind would study such a hard subject; this candidate must be a crazy type and do crazy things should he work in a high-pay job". Such expected reaction in turn feeds back to the belief that, even for high-talent students, it does not pay off to differentiate and take the hard subject.

As this example illustrates, forward-induction reasoning is context-dependent, i.e. it depends on what are the shared assumptions about beliefs within the reference group. This may have consequences that appear counter-intuitive to the untrained mind: More restrictive shared assumptions about beliefs may allow for outcomes that are ruled out by less restrictive ones! Thus, "context-free" forward induction reasoning (which is well understood from previous theoretical work) does not necessarily yield the most permissive results and cannot be used to obtain robust predictions.

Pierpaolo Battigalli (Department of Economics) and Amanda Friedenberg (Arizona State University) make these concepts precise in Forward Induction Reasoning Revisited (Theoretical Economics, Volume 7, Issue 1, January 2012, Pages 57-98, doi: 10.3982/TE598) using the tools of "Epistemic Game Theory", the mathematical analysis of players' beliefs about each other in games. In particular, they study the following question: What patterns of behavior are consistent with forward-induction reasoning from the point of view of an analyst who does not know the "context"? The general answer is given by a new solution concept called "Extensive-Form Best Response Set" (EFBRS). Using the properties of EFBRSs, it is shown how the answer depends on the particular game being played.

For example, in generic games with complete and perfect information, all and only the un-dominated Nash equilibrium outcomes are consistent with forward-induction reasoning. If there is only one such outcome, as in the well-known Centipede game, then this must coincide with the traditional "backward-induction" solution of introductory textbooks. In this case, forward-induction reasoning yields the backward-induction outcome whatever the context. But in games with multiple (un-dominated) Nash equilibrium outcomes, such as the so called Chain-Store game, different social contexts support different outcomes.