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Profits one agent; defect or cooperate
1.6
defect
cooperate
1.4
1.2
1
C
n
+2
D
n
+1
0.8
C
n
+2
C
n
+1
0.6
C
n
+1
D
n
0.4
D
n
+1
D
n
0.2
0
0 1 2 3 4 5 6 7 8 9
number other cooperators; myopic biddders
Fig. 4.
Profits cooperate or defect (a) and generalized payoff table (b)
and to verify whether the conditions of the
nIP D
hold like above. If this is
the case, then there is a strong indication of the equilibrium outcome for more
advanced strategic bidding.
6
Perspectives for the Bidders
In Section 5, we have argued that, in the limit, agents attempting to exploit the
complementary value of future auctions will lead to suboptimal profits due to
the prisoners' dilemma type nature of the domain. Does this however mean that
agents ultimately cannot benefit from (machine) learning?
The results of Section 4 are presented for
bidmodifier
=0
.
1. This is a rea-
sonable first choice, but agents can individually benefit from a better choice.
In Figure 5(a), we show results for the first 7 agents using a strategic bidding
strategy and the last three agents using a myopic bidding strategy as usual. How-
ever, the first two strategic agents use a bid modifier of
bidmodifier
+0
.
1. The
non-strategic bidders are, of course, worse off but the first two most aggressive
bidders outperform their more conservative rivals.
In Figure 5(b) we again present results for 10 agents. Of these, 8 use an aggres-
sive bid strategy with the standard
bidmodifier
=0
.
1 (overbid) and one uses a
higher
bidmodifier
of 0
.
2 (rampant). The last agent is a myopic bidder. Results
give the mean profits as function of the number of epochs learned. We plot results
for the usual learning rate
α
=0
.
1 and a high(er) learning rate of
alpha
=0
.
2.
Study of Figure 5(b) learns that more aggressive overbidding, as expected
from Figure 5(a), is a profitable strategy. Additionally, a better choice in the
learning rate (in this case higher ), results in higher aggregate profits as agents
more quickly adapt towards the equilibrium strategy.
The above two results are of great importance in real-life models or more
stochastic domains. We claim in Section 5 that we can predict the equilibrium
