Experiments

There are six agents and two types of goods in our experiments. Each agent starts with a random endowment of both goods. Prices are in units of good 2; thus, all auction activities are for good 1.

Each agent has the same CES utility function as defined in (1). We let $\alpha_j =1$ for all j, and $\rho = {1 \over 2}$, and so the utility function becomes $U(x)=\biggl(\sum _j (x_j)^{1 \over 2}\biggr)^2$. According to (2) and (3) we have reservation prices as

We test three types of agents: the competitive agent, price modeling agent, bidder-modeling agent. We put these agents in three kinds of environments where all other agents are: (1) competitive agents; (2) price modeling agents; (3) bidder-modeling agents. A competitive agent does not use any information in the auction market. It chooses its action based on its individual optimization problem. A price modeling agent uses the previous clearing prices to predict the clearing price in the next period and then chooses its best-response bid. A bidder-modeling agent uses other agents' bidding history to predict their next bids and choose its best response bid.

In each of the three environments, we randomly configure the initial endowment of all agents. We compare the performance of the first agent for each type it assumes. Our results are averaged over 6 different sets of initial endowments.

Figure 6 presents results for an environment where all other agents are competitive agents. When Agent 1 chooses the price modeling strategy, at the beginning it performs better than behaving competitively. However, this advantage goes away over time when the price modeling agent's bid distorts the market clearing price and the auction closes prematurely. Similar results are seen when the agent adopts the bidder-modeling strategy. In Figure 7, where other agents are price modeling agents, we observe different results. The main difference is that when Agent 1 adopts the bidder-modeling strategy its performance is higher than using other strategies at least for the first 20 rounds. The clearing price strategy outperforms, slightly, the competitive strategy in the earlier rounds but then leads to worse performance than the competitive strategy when it causes the market to close before all trading opportunities have been explored.

  

Figure: Agent 1's performance when others are competitive agents

  

Figure: Agent 1's performance when others are price modeling agents

  

Figure: Agent 1's performance when others are bidders modeling agents

Figure 8 shows the results when others are bidder-modeling agents. In this case both modeling strategies perform worse than the competitive strategy almost all of the time. This is probably because all the agents are trying to model each other rather than bidding truthfully. This leads to some sub-optimal equilibrium, as we have discussed in a previous paper [Wellman & Hu1998].