Value Competition

Mixed Nash continued

Following up on the four-person game analyzed in the previous post...

Memo to self: If the Pascal-Bentham-Whitman-Nash type that optimizes in two-player games and holds its own against egoists is a truly groovy type, it should also optimize and be an evolutionarily stable type in the four-player game in which you play either 2 or 10 and get either $2 or $10 except that if all four choose 10 no one gets anything.

As a two-person game, this is a leadership game, and I'm morally sure (that is, I think I know but don't really know) that P-B-W-N will optimize because the game is similar enough to ones I have analyzed.

As a four-player game...well, I haven't really thought about multi-player games for P-B-W-N purposes, basically because the tech gets out of my league...

A note or two...the .928 probability of playing 10 that is mixed Nash for four egoists is decidedly suboptimal...a little SAT-style plug-in suggests that the optimal level of playing 10 is somewhere between .5 and .75...so P-B-W-N if it is an optimizing type in the 4-player game should play 10 at that lower level...to meet the criterion of being an evolutionarily stable strategy, it should also be resistant to egoism...

I'm genuinely interested (i.e., no moral certainty here) as to whether P-B-W-N is optimizing and an ESS in the 4-player game...a to-do for when some time opens up after getting my SBE paper for 3/1 done...

 

 

P/B/W/N compared to P/B/N

Warning: This post is wonky.* 

In order to optimize outcomes in a 2 x 2 game, how much do we need to have players who are W (W = Whitman = non-calculating) as well as N (N = Nash = calculating)?

One plausible but I believe unsatisfactory answer: We don't need W at all as long as the N side is ashamed as well as egoistic.  I see two problems with a pure N player.  First, relying on N with shame across the board is riding the shame horse very hard, considering that shame already enters into the decision-making process (as part of a player's Pascal side).   It would be better if shame isn't used twice unless it has to be.  Second, my intuition is that a purely calculating N player with no W propensity to engage in actions without calculation fails to give the other player enough information to avoid mixed strategies and suboptimal outcomes.  To confirm that it would be necessary to do the game by game analysis, but I'd be surprised if N with shame alone is enough to do the trick.

A third reason W is valuable is that in many games we do not need N with shame.  In those games, W with given propensities of Pascal or Bentham play plus egoistic N will solve the game.  Not all games work that way; notably, in the Prisoner's Dilemma one must have shame on the part of the calculating player to lift cooperation to a high level.  But in the significant majority of games, the shame already present within Pascal will solve the game without the need for an additional dose of shame in Nash. 

A fourth reason to suspect the reality of W is empirical.  If W operates, people sometimes "just do it" rather than calculate.  That "just do it" behavior is very likely more consistent with the results of lab experiments than a view of people as having N without W.

*Credit to Paul Krugman for the warning.

Optimal Routes

Thoughts provoked by walking through Washington Square Park to NYU yesterday by one route and then walking back by another route:

Faced  with a decision as a walker about turning toward my destination or going straight toward it, I tend to turn.  That tendency is sufficiently strong that it often results in my taking different routes when I walk from A to B than when I walk back from B to A, even if I walk between the two points a fair amount and even if one route is better.

When I drive, there's a somewhat different anomaly in my route choices: I tend to be overly reluctant to double back.  One result of that tendency is that I took quite different routes to and from work for two years in a job I had in the 1980s in which my commute started on a one-way street that forced me to go in one direction before turning.

I think that these tendencies for me as an individual to deviate from optimality can be explained with a combined evolutionary psychology and value competition story.  The variation in routes that results from a "turn" tendency and an opposing "stay straight" tendency, even if excessive from the point of view of the individual's welfare, has beneficial properties for social organisms like people, or for that matter chimpanzees or fish.  Calling "turn" a value competing with "stay straight" (or calling "don't double back" a value competing with "double back") may seem like a stretch. But I don't believe it is; the function of "turn" and "stay straight" in relation to individual and collective decision is quite parallel to that of "id/pleasure" and "superego/duty" and other dichotomies in relation to individual and collective decision.

Out of these reflections, a VC prediction: Behavioral experiments in humans and other social animals will show a substantial number of individual subjects who deviate from optimal routes because of a "turn" proclivity or value and a very comparable number of other individual subjects who deviate from optimality because of a "stay straight" proclivity or value.  (In asocial animals, on the other hand, individual deviations from rationality should be less, given the lack of benefit such deviations confer on the group.)  The gist of the prediction: equality in the numbers of those with a suboptimal tilt toward "turn" and a suboptimal tilt toward "straight."

Logistics Values

Last Thursday my Supply Chain Management and Marketing Sciences colleague Ben Melamed presented a paper he wrote with two RBS colleagues, Yihong Fan and Yao Zhao, together with Yorai Wardi of the Georgia Institute of Technology.  The paper, "IPA Gradients in Stochastic Flow Models (SFM) for Make-to-Stock Production-Inventory Systems with Backorders under the (R, r) Policy," models a production facility's decisions to suspend and resume the replenishment of product to an inventory facility in terms of a mathematical process called Infinitesimal Perturbation Analysis (IPA), in which derivatives are calculated through formulas that should ideally be comprehensive, unbiased, nonparametric, and computationally speedy.  http://www.business.rutgers.edu/files/ben_ipa.pdf

I lack the mathematical expertise to reflect usefully on possible value competition interpretations (such as value-based tilts in favor of discrete modeling over stochastic flow modeling, or the reverse) of the technical matters treated in the paper; hence, my notes here relate to modeling in value competition terms the business situation that that the paper models in mathematical terms.

The situation with the production facility and the inventory facility can be assumed to involve preferences by managers in both facilities that are in part in conflict with preferences in the other facility (for example, both sides may have an interest in smoothing activity at their facility and hence increasing work load variance at the other facility) and with those of the enterprise as a whole (for example, both sides may have incentives to collaborate in maintaining unduly high inventory levels to the detriment of enterprise profitability).  From a VC modeling perspective, the basic issue here as always is whether there are competing values that cross-cut the sometimes dysfunctional preferences of the sides and motivate agents to come up with policies in the interests of the total system.  "Logistics values" of believing in technical solutions to supply chain issues and "team coordination values" of believing in management solutions can serve that role well, as long as they meet the following two conditions: 1) the values cross-cut rather than coincide with being on the production or inventory side (plausible, as long as one side isn't a purely "tech" unit and the other a purely "people" unit); 2) the values have bite, so that commitment to "logistics values" or "team coordination" values will move managers to take a different stand or a more intense stand than they would have taken based on their production or inventory interests alone (plausible, though not in all situations).

Some modeling issues I'd need to think about more in a paper on the production-inventory situation: 1) the basic VC model of the Eastman-Collier paper involves the right answer-social welfare being immanent in preferences rather than being external and objective; I believe the VC model can be modified to deal effectively with partially or totally objective, external social welfare functions of the kind that would seem applicable to the production-inventory case, but that's an issue; and 2) the "logistics values" and "team coordination values" agents could be modeled in terms of individuals who belong to competing groups, along the lines of the politicians and political parties in Eastman-Collier, but it might be more realistic and fruitful to model them in terms of competing centers within individual managers that might not be recognized consciously by the manager as competing with each another.