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Note that we can see from these coefficients that it improves an agent's score some-
what to have clients with high entertainment premiums, it hurts performance to be in a
game with high flight prices, it hurts to have clients that prefer long trips (particularly
when other agents' clients do as well), and finally, having clients with high hotel premi-
ums improves score. Applying the score adjustment formula to the 2004 finals yields a
reduction in variance of 9%.
5.2
Results
A detailed presentation of an earlier snapshot of our experimental results, along with
game-theoretic analysis, is provided elsewhere [5]. Here we present only a brief sum-
mary. A final account based on the ongoing simulations is forthcoming.
Analysis of the TAC
↓
1
“game” tells us which strategy performs best assuming it
plays with copies of itself. We included a strategy (S34) designed to do well in this
context: it shades all hotel bids by a fixed 50% rate. This indeed performs best, by
about 250 points, since the result is very low hotel prices. However, the profile is quite
unstable, as an agent who shades less can get much better hotel rooms, but still benefit
from the low prices. Thus, this is not nearly an equilibrium in the less-reduced games.
With over 70% of profiles evaluated, we have a reasonably complete description of
the two-player game, TAC
↓
2
, among our 40 strategies. At this point in the experiment,
we identified ten candidate strategy profiles that represent pure
-Nash equilibria, for
27. Four of these were confirmed, meaning that all deviations had been evaluated.
We also identified 41 symmetric mixed-strategy profiles in equilibrium. Less than 1/3
of the considered strategies participate with probability exceeding 0.15 in some equi-
librium found.
Results for TAC
≤
↓
4
must be considered relatively tentative. Based on the profiles eval-
uated, we can identify a few good candidate equilibrium mixtures over pairs of strate-
gies. Further simulation in the next few months may confirm or refute these, or identify
additional candidates. With a few exceptions, strategies and combinations evaluated as
stable in TAC
↓
4
.
Analysis of the reduced games does validate the importance of strategic interactions.
As noted above, the best strategy in self-play, S34, is not nearly a best response in most
other environments, though it does appear in a few mixed-strategy equilbria of TAC
↓
2
tend to produce similar results in TAC
↓
2
.
Strategy S34 achieves a payoff of 4302 in self-play. For comparison:
-
The top scorer in the 2004 tournament,
Whitebear
, averaged 4122.
-
The best payoff we found in TAC
↓
2
in a two-action mixed-strategy equilibrium
candidate is 4220 (and this involves playing S34 with probability 0.4).
-
The best corresponding equilibrium payoff we have found in TAC
↓
4
is 4031. No
such equilibrium includes S34.
6
Walverine 2005
Given all this simulation and analysis, how can we determine the “best” strategy to
play in TAC? We do have strong evidence for expecting that all but a fraction of the
