Market behavior and performance of different strategy evaluation schemes

Strategy evaluation schemes are a crucial factor in any agent-based market model, as they determine the agents’ strategy preferences and consequently their behavioral pattern. This study investigates how the strategy evaluation schemes adopted by agents affect their performance in conjunction with the market circumstances. We observe the performance of three strategy evaluation schemes, the history-dependent wealth game, the trend-opposing minority game, and the trend-following majority game, in a stock market where the price is exogenously determined. The price is either directly adopted from the real stock market indices or generated with a Markov chain of order $\le 2$. Each scheme’s success is quantified by average wealth accumulated by the traders equipped with the scheme. The wealth game, as it learns from the history, shows relatively good performance unless the market is highly unpredictable. The majority game is successful in a trendy market dominated by long periods of sustained price increase or decrease. On the other hand, the minority game is suitable for a market with persistent zigzag price patterns. We also discuss the consequence of implementing finite memory in the scoring processes of strategies. Our findings suggest under which market circumstances each evaluation scheme is appropriate for modeling the behavior of real market traders.

Figure 1

(Color online) The performance of the three strategy evaluation schemes are observed when the price is exogenously given by the real stock market indices: the HSI closing prices from December 31, 1986 to May 25, 2010 and the KOSPI closing prices from July 1, 1997 to May 25, 2010. Other market parameters are given by $N=10000$, $m=2$, $s=2$, and the initial wealth of each agent is set equal to five times the initial stock price to encourage activity. The number of strategy-switching agents is shown in the cases of (a) WG, (b) MinG, and (c) MajG. The average wealth gained by each strategy evaluation scheme is shown for both (d) HSI and (e) KOSPI. For reference, the stock market indices are shown along in black.

Figure 2

(Color online) The sample mean of the average wealth gained by each strategy evaluation scheme at the 1000th time step, measured for various values of the probability of price increase $p_{\uparrow }$ and averaged over 1000 samples. The other parameters are given by $N=10000$, $m=2$, and $s=2$. The error bars indicate standard deviation of the average wealth from the sample mean. Note that the lines are guide to the eyes.

Figure 3

Insets show in purple examples of price data generated by different values of $p_L$ and $p_S$. Higher values of $p_L$ indicate greater likelihood for long-term trends, and higher values of $p_S$ indicate longer zigzag oscillations.

Figure 4

(Color online) Diagrams showing performance of strategy evaluation schemes for different values of $p_L$ and $p_S$, with memory size $m$ varied. The upper two diagrams indicate the average wealth of agents using each strategy evaluation scheme, for (a) $m=2$ and (b) $m=3$. The lower two diagrams represent the chance of each evaluation scheme achieving the highest average wealth, for (c) $m=2$ and (d) $m=3$. Other parameters are given by $N=10000$ and $s=2$, with the average wealth measured at the 5000th time step. As the ternary plot on the right shows, superior performance is indicated by greater weight put on the scheme’s representative color. We use the average wealth of agents and the chance of attaining the highest average wealth to visualize the relative performance of a strategy evaluation scheme. Note that the region where MinG or MajG is successful increases as $m$ is increased from 2 to 4. We observed the same trend when $m$ is further increased to 10.

Figure 5

(Color online) The data points represent the average wealth gained by each strategy evaluation scheme shown for different sizes of score memory $T$, while the dashed lines correspond to the average wealth obtained by the original infinite-score-memory evaluation schemes. The average wealth is measured at the end of the observation period, which is (a) from December 31, 1986 to May 25, 2010 for the HSI closing prices and (b) from July 1, 1997 to May 25, 2010 for the KOSPI closing prices. Parameters other than the score memory are given by $N=10000$, $m=2$, $s=2$, and an agent’s initial wealth is set equal to five times the initial price.

Figure 6

(Color online) Each strategy evaluation scheme’s chance of reaching the highest average wealth are shown for different values of the score memory size $T$, in an artificial market whose price is generated by a Markov chain of order 2. Refer to the ternary plot in Fig. 4 for the meaning of each color. The upper three diagrams compare the performance of the original WG, DMinG, and DMajG for (a) $T=10$, (b) $T=100$, and (c) $T=1000$. The lower three diagrams compare the performance of DWG, DMinG, and DMajG for (d) $T=10$, (e) $T=100$, and (f) $T=1000$. Other parameters are given by $N=10000$, $s=2$, $m=2$ with the average wealth measured at the 5000th time step.