Today, in Managerial Economics, the professor talked about Game Theory. The subject made me hark back to "Austrian Economics and Game Theory: a Stocktaking" at http://tinyurl.com/2vyna. I also thought of *The Games Economists Play*, by Murphy, at http://tinyurl.com/2vgoq. I see some interesting elements of value in game theory. Fundamentally, it appears to be strongly influenced by praxeology, human action, as is indicated in the basic Prisoner's Dilemna. Furthermore, though Murphy notes that game theory has been used to justify state intervention (because the Nash-equilibrium is not the optimum cooperation), there are also those who have used game theory to argue against State intervention. See *The Possibility of Cooperation* by Michael Taylor. Anyways, a cruel alternative to prisoner's dilemna occured to me in the class. This was not really my own creation, but I remembered it from Baldur's Gate II. * If both push their buttons, both die. * If neither push their buttons, both die. * If one of them pushes their button, but the other doesn't, the one who did not push the button dies. * Each of them has one hour to decide whether or not to push the button * Neither of them can see whether the other is about to or has pushed his or her button Obviously, this is a one-shot "game", so we need not considder repeated games. The following outcome table emerges (in each cell, the first listed outcome is what happens to A, the second listed one is what happens to B, given the inputs, which are the row and column headers: A --------------------------------------------- | | Push | Don't Push | |-------------|------------|----------------| | Push | D,D | D,L | B |-------------|------------|----------------| | Don't Push | L,D | D,D | --------------------------------------------- (clearly, this is a game that you don't want to play) At first, it appears that there are only three possible outcomes (I will not differentiate between them both dying from them both pushing, or them both dying from them both not pushing): D,D: A dies, B dies D,L: A dies, B lives L,D: A lives, B dies -------------------------- The Game Theorist Analysis -------------------------- The game theorist analysis, I would guess, would go as follows. A would prefer that A lives, B that B lives. A's analysis of the situation would go something like this: If A does not push the button, A will most certainly die, whether B pushes the button or not. However, if A pushes the button, he will live if B does not push the button, though he will die if B also pushes the button. It is at least conceivable to A -- albeit unlikely -- that if he pushes the button, he will survive. B's analysis proceeds in exactly the same manner. Thus, if each wishes for himself to live, both A and B will push the button. The Nash equilibrium is that they would both push the button, and thus that they should both die. In short, if they each picks the strategy that they see as allowing for the possibility that their-selves could live, they both will die. According to this standard line of game theory reasoning, it is impossible that either of them could live. -------------------------------------------------- Possible Psychological Ordinal Preference-Rankings -------------------------------------------------- In the following, I will list possible ordinal preference rankings for A and B in a list, with the most preferred outcome at the top of the list, progressively going towards less preferred outcomes. This seems to be simple, but in fact the list becomes rather long once you realize that it is perfeclty *possible* that A could prefer D,D, or that A could be indifferent between the three outcomes, or between two ofthe outcomes. In the case where there is indifference between two or three outcomes, they are listed side-by-side In the case where A is indifferent between two or three outcomes, that indifference cannot explain why he either pushes a button or does not push a button. I am aware that preference can only be revealed through action, and that indifference *cannot* be illustrated by action. These ordinal preferences I am listing are not all praxeological preferences, because action can only illustrate preference, not indifference. They are, rather, preferences from a prior psychological point of view. Praxeological ordinal rankings can only be revealed via action. This is an exhaustive list of all possible ordinal rankings. If I am either A or B, I know which ranking I prefer: 1 2 3 4 5 6 D,L D,L L,D L,D D,D D,D L,D D,D D,D D,L D,L L,D D,D L,D D,L D,D L,D D,L 7 8 9 D,L L,D D,D L,D D,D D,D D,L D,L L,D 10 11 12 L,D D,D D,D D,L D,L L,D D,L L,D D,D 13 D,D D,L L,D Immediately, a problem with game-theory is apparent. It goes beyond economics and into psychology. From all I've heard, game theory seems to concern itself only with one possibility: A would want to live, and B would want to live. This cannot be an acceptable assumption. -------------------------------------------------- Possible Psychological Ordinal Preference-Rankings --------------------------------------------------
From a praxeologically significant standpoint, ordinal preference rankings can only be revealed through action. However, in this case, it can only be deduced what one *does not* prefer based on one's button pushing:
If A pushes the button, what can we deduce? Not much, unless we make certain assumptions. Strictly speaking, if A pushes the button, all that we can deduce is that his highest valued outcome was *not* D,L -- that he dies and B lives. There are two possible reasons why A pushed the button: (1) he preferred that both of them should die (D,D); or (2) he preferred that he should live and B should die (L,D). Thus, from the following actions by A or B, in this case, we can only deduce what they do not prefer: A pushes button: Does not prefer D,L A does not push button: Does not prefer L,D B pushes button: Does not prefer L,D B does not push button: Does not prefer D,L --------------------------------- Some Problems with Game Theorists --------------------------------- It seems to me that game theorists -- not game theory itself -- have some problems from the start. Namely, they go beyond economics and into psychology, making assumptions which can hardly be assumed to be univeral. The game theorist would assume that A would want the L,D outcome and B would want the D,L outcome. However, why does that need to be so? Let's consider one possible preference which everyone seems to reject off-hand: D,D. Let's say that A and B were married. It is possible to think that both, then, would place the highest value on outcome D,D, as both know that neither would want to live without the other. Once we accept that the fact that it is possible that A and B may have any of the listed 13 value scales, the normal game theory analysis is completely exploded, and this seemingly "simple" example becomes unbelievably complex. http://groups.yahoo.com/group/mises Sponsor: www.mises.org Yahoo! Groups Links <*> To visit your group on the web, go to: http://groups.yahoo.com/group/mises/ <*> To unsubscribe from this group, send an email to: mises-unsubscribe@yahoogroups.com <*> Your use of Yahoo! Groups is subject to: http://docs.yahoo.com/info/terms/ ----- End forwarded message ----- -- Churchill, Winston Leonard Spencer --On the eve of Britain's entry into World War II: "If you will not fight for right when you can easily win without bloodshed; if you will not fight when your victory will be sure and not too costly; you may come to the moment when you will have to fight with all odds against you and only a precarious chance of survival. There may be even a worse fate. You may have to fight when there is no hope of victory, because it is better to perish than to live as slaves.