If you are interested in those kind of social dynamics, I highly recommend studying game theory—it’s absolutely full of surprising results and predictions.
In one class, we proved that for a certain model of soccer penalty kicks, if a kicker got better at shooting (increased the chance of scoring, ceteris paribus) but only in one direction (left or right), he actually was less likely to score because it was easier for the goalie to predict which side he would favor.
That doesn’t sound right. Why couldn’t you simply choose to keep on randomizing 50/50? (Or better yet, calculate an optimal mixed strategy which should be at least as good as randomizing. But my immediate reaction is just generated by the heuristic that capability improvements should never hurt you because you can always choose to go on doing what you would have done previously.)
Ah, of course, I forgot a prepositional phrase: he actually was less likely to score on that side because it was easier for the goalie to predict which side he would favor.
(Incidentally, this proposition has been empirically tested in G.C. Moschini, Economics Letters 85 (2004) 365–371)
However, we do have to be careful in games of strategy in selecting what we call capability improvements. Increasing my payoff in a single cell can change the relationship between cells, preventing me from credibly committing to a particular strategy and thereby diminishing the outcome of the game.
As an example, imagine we have a game defined as follows:
(U,L) ⇒ (1,1)
(U,R) ⇒ (0,0)
(D,L) ⇒ (0,0.9)
(D,R) ⇒ (1,0)
where the pairs are (x strategy, y strategy) mapped to (payoff to x, payoff to y).
The unique Nash equilibrium is (U,L), so each player receives a payoff of 1.
Now “improve” player y’s capabilities by making (U,R) ⇒ (0,1.1). Now there is no equilibrium in pure strategies, and the unique mixed strategy equilibrium is: Pr(U) = 0.9, Pr(L) = 0.5. Expected payoff to the “improved” player is 0.99, and to the other player 0.5, both down from their previous equilibrium values of 1 each, and the magnitude of the effect damaging player y increases as her payoff to (D,L) decreases (derivations available on request).
Of the top of my head, I suspect your heuristic applies in zero-sum games, but not necessarily elsewhere. Unless the players could read each other’s source code...
Related: here’s a fascinating recent Reddit thread about generating random numbers with your brain while playing poker. I’m curious if the LW community can come up with better ways, because the ones proposed there strike me as inadequate. IMO, memorizing a longish string of random digits beforehand was the best strategy proposed.
If you are interested in those kind of social dynamics, I highly recommend studying game theory—it’s absolutely full of surprising results and predictions.
In one class, we proved that for a certain model of soccer penalty kicks, if a kicker got better at shooting (increased the chance of scoring, ceteris paribus) but only in one direction (left or right), he actually was less likely to score because it was easier for the goalie to predict which side he would favor.
That doesn’t sound right. Why couldn’t you simply choose to keep on randomizing 50/50? (Or better yet, calculate an optimal mixed strategy which should be at least as good as randomizing. But my immediate reaction is just generated by the heuristic that capability improvements should never hurt you because you can always choose to go on doing what you would have done previously.)
Ah, of course, I forgot a prepositional phrase: he actually was less likely to score on that side because it was easier for the goalie to predict which side he would favor.
(Incidentally, this proposition has been empirically tested in G.C. Moschini, Economics Letters 85 (2004) 365–371)
However, we do have to be careful in games of strategy in selecting what we call capability improvements. Increasing my payoff in a single cell can change the relationship between cells, preventing me from credibly committing to a particular strategy and thereby diminishing the outcome of the game.
As an example, imagine we have a game defined as follows:
(U,L) ⇒ (1,1)
(U,R) ⇒ (0,0)
(D,L) ⇒ (0,0.9)
(D,R) ⇒ (1,0)
where the pairs are (x strategy, y strategy) mapped to (payoff to x, payoff to y).
The unique Nash equilibrium is (U,L), so each player receives a payoff of 1.
Now “improve” player y’s capabilities by making (U,R) ⇒ (0,1.1). Now there is no equilibrium in pure strategies, and the unique mixed strategy equilibrium is: Pr(U) = 0.9, Pr(L) = 0.5. Expected payoff to the “improved” player is 0.99, and to the other player 0.5, both down from their previous equilibrium values of 1 each, and the magnitude of the effect damaging player y increases as her payoff to (D,L) decreases (derivations available on request).
Of the top of my head, I suspect your heuristic applies in zero-sum games, but not necessarily elsewhere. Unless the players could read each other’s source code...
Related: here’s a fascinating recent Reddit thread about generating random numbers with your brain while playing poker. I’m curious if the LW community can come up with better ways, because the ones proposed there strike me as inadequate. IMO, memorizing a longish string of random digits beforehand was the best strategy proposed.