In addition to receiving a description of the payoff function (Equation 1), individuals were also given a payoff table
indicating their payoff for each level of private contribution and a level of aggregate contributions by others.
The first, we construct a payoff table
The payoff table
for each game you play will be shown on your computer screen.
To see the advantage of being the leader in a Stackelberg game, consider a simple game with the payoff table
as shown in figure 3.
Table 1 Win-Lose Table A B C D E Total units Proportion Proportion Proportion Proportion (coins) of Players of Players of Players of who staked in a who who who experience single play experience experience experience less than session ** better than between 80 between 60 60 per cent 100 per & 100 & 80 per return of cent return percent cent return total of total return of of total amount amount total amount staked staked amount staked staked 2000 29% 46% 22% 3% 3000 25% 54% 20% 1% 4000 22% 61% 17% 0% 5000 19% 66% 15% 0% 6000 17% 71% 12% 0% 8000 14% 77% 9% 0% 10000 11% 82% 7% 0% ** Assumes all games played on a single line with one coin staked per game Table 2 Payoff Table
for "Red, White & Blue" Slot Machine Win Pays Combinations Probability Red 7, white 7.
In my previous column (Jan/Feb 2005, The Physician Executive), I discussed the use of the payoff table
as a tool to assist in making rational choices when faced with this uncertainty.
Subjects use the average payoff table
window to select their choices.
Experimental subjects were confronted with identical payoffs: 50 cents for each player whenever the first mover chose [bar]T (corresponds to choosing alternative A in the experimental payoff table
in Appendix C); $1.
A built-in payoff table
sets the amount a player gets for a given winning combination.
In the first part of the experiment, subjects were given a Payoff Table
showing the individual profits accruing to any participant as a function of the number of entrants and then asked to make only an entry decision.
This problem is also apparent in Holt's payoff table
, where any output pair summing to 24 constitutes a CCE with a profit level of 45.
Each party's payoff table
has roughly 200 possible combinations of X and Y over which he or she can bargain.