Table 1. Notation and parameter values An experimental study of adaptive behavior consumption good, using the same technology (see below). Time is divided into discrete periods. At the beginning of each period, each firm has to decide how many units of the perishable consumption good to produce. The production costs per unit are constant, and identical for all firms. The production decided upon at the beginning of the period is available for sale in that period. The firms also decide upon a number of information or advertising signals to be sent into the population, communicating the fact that they are a firm offering the commodity for sale in that period. Imagine the sending of letters to addresses picked randomly from the telephone directory. The costs per information signal sent to an individual agent are constant, and identical for all firms. The price of the commodity is fixed, invariant for all periods, and identical for all firms and consumers. The choice of the number of units to be produced, and the number of infor- mation signals to be sent, is restricted to a given interval. Consumers in this economy are simulated by a computer program. In each period, when all firms have decided their production and signaling An experimental study of adaptive behavior Hence, we draw a 3-D ‘immediate profit landscape’, showing all points that lead to positive immediate profits as an ‘island’. If, on the one hand, firms invest in order to build up a market, this island will grow. On the other hand, a firm’s market may collapse if it does not signal enough. For ex- ample, it may be tempting for players to seek maximization of their im- mediate profits, i.c., to search for the peak in their immediate profi landscape. What would happen then? Analyzing every single instance in which an individual player had to make a decision in our experiments, i turns out that very often the global maximum of immediate profits is a corner solution with signaling at zero and production equal to the demand generated. This was the case 84% of the time in the first series of experi ments. Hence, if a firm would try to maximize its immediate profits, its market will shrink away under its own eyes in most cases. An example of this effect is shown in Fig. 1, where the dot indicates the action chosen by the player considered, and where the other players each send 750 signals. Figure 2 shows an example within the same environment of the opposite positive feedback effect, where a firm builds up its market by maximizing its Table 3. Predictions hill climbing closer he gets to the optimum, the louder they are expected to shout. Therefore, after two trials he can compare the levels of payoff, and shoot next time in the neighborhood in which the yelling was loudest. In other words, if an action eads to a worse outcome than the previous one, it is rejected as a new starting point. Hill climbers do not use any knowledge of the structure of the game, or of the payoff function. They are myopic local improvers, walking blindly in the direction of the experienced gradient in their payoff landscape. Hence, hill climbers rely completely upon the con- tours of the payoff landscape, whereas direction learning takes place di- rectly in the space of actions. A deterministic variant of hill climbing would give the predictions presented in Table 3. In our experimen there is one problem with hill climbing: as we showed in Section 2, the hills may change over time, even considering constant actions of ae A | ne | ee i ne: ne) a a: nae aa: (a; he Table 4. Comparison equilibrium, averages, and standard deviations (subjects—sessions) 2° Throughout the paper, unless otherwise stated, we adhere to the following policy when computing averages. When the objective is to characterize the behavior of the individual players, or the differences between (categories of) individual players, we take the averages over the periods that a player was active, i.e., until the end of the session or until he went bankrupt, whichever came first. When we want to characterize the average actions and outcomes for one or more sessions as such, e.g., to compare it with the theoretical benchmarks computed, we average over all players, taking zero values for the actions and outcomes of bankrupt players. An experimental study of adaptive behavior adaptively. As we see, the players learn to choose actions that are on averagi close to a symmetric equilibrium, but there are large differences betwee these actions. Figure 4 shows the distribution of the individual players’ sig naling and production levels, averaged over the periods 81—130 (with zer« values for bankrupt players). The arrow indicates the symmetric game-the oretic equilibrium given above. The straight line with slope (p — c)/k serve: as a benchmark. All combinations of production and signaling above i necessarily lead to negative profits. If every unit produced is actually sold, thi net revenue is given by the price minus production costs per unit, multipliec by the production level: (p —c) - z. Dividing that number by the cost of < signal (k) gives the number of signals beyond which profits can never bi positive. We will return to these differences between the players in Section 4.c iene eal aaet inated», nat iciasidi i iieatiiiatiiadineatiniiniaa eden Figure 5 clearly shows the asymmetry between these cases. As explaine above, it seems that the players are more reluctant to decrease their pro duction level when it is too high, because they understand that productio should be higher than average demand; the players are less boundedly ra tional than learning direction theory assumes. Checking the players one b one, we find that 58 out of 66 subjects more often follow the learnin direction theory hypothesis in the case in which production is less tha demand, than in the case in which production is higher than demand. Als it turns out that a// players, without any exception, on average overproduc« with the overall average production 1.20 times average demand. An experimental study of adaptive behavior as well as his lookahead payoff (taking into account also the future profits related to his current sales level) had increased, or both had decreased. When we consider only the other 29% cases of opposite gradients, the cases in which myopic hill climbing and lookahead hill climbing predict a dif- ferent change in signaling, we find that on average the players are inclined only slightly towards looking ahead; in 53.2% of those cases they follow the prediction of lookahead hill climbing, and in 48.8 the prediction of myopic hill climbing. ?3 It should be stressed that the two curves have a different time scale. Tinkering with the speed of adjustment of the players (e.g., adjusting the speed itself as well), would yield a better fit along this dimension, but that is not our objective. We use an identical and constant (but stochastic) low adjustment speed for all players. HOLE SCUClal PsyCHuOlwslldal ICAaAluUle, We have seen that the 2-step model we proposed does not perfectly lescribe the behavior of the players. But at the same time, the attraction of the model is its simplicity. A question, then, is whether the time-pattern of he average behavior of the players in the experiments fits the pattern predicted by this simple model. In Fig. 7 we present the average behavior of |1 simulated sessions with 6 players, and the average signaling levels ob- served in the experiments. As we see, the average signaling level not only sonverges to the same level, but it also shows a similar initial dip. 23 boundaries for which the difference between the average signaling in the middle category and the other two categories combined is maximized.*’ We will use these three categories in our subsequent analysis, to see whether we can identify qualitative differences in the adaptive behavior between these three groups of players. The numbers in Fig. 8a, b give the values of profits and signaling respectively for the observations next to the boundaries. Table 5 illustrates this categorization further by giving the average sig- Table 5. Averages for the three categories Observation 7. When hill climbing, category I players look ahead mos often. Category II players do so least frequently. Table 6 shows the frequencies with which the players go for immediate profits, and with which they look ahead in those cases in which the hil climbing hypothesis points to opposite directions. We observe that the differences in frequencies between the categories are not large. Category I players look ahead less frequently than category I players (significant a 0.9%; 1-sided Wilcoxon test), and also less frequently than category H Table 6. Frequencies myopic vs. lookahead hill climbing Observation 8. Both production and signaling levels in the first period are concentrated on focal points. Further, the individual players’ sales in later periods are positively correlated with their sales in the initial periods. The correlation coefficient between the 66 individual players’ average sales levels in the periods 1-10 and the periods 81—130 (taking zero values for bankrupt players) is 0.55 (significant at 0.0% level; 1-sided t-test). In the first period, the players have very little information to guide their Table 7. Shrinking customer pool by not signaling, with production >0 Table 8. Relative frequency switching to voluntary inactivity Table C.1. Summary data individual players Table C.2. Session averages
