So, how easy is it to get a speculative asset bubble?
Students allocate their wealth between cash and a dividend-paying asset, whose price is determined in a competitive market. Even with all information (except the rationality of other players) common knowledge, it is common to get speculative asset bubbles with transaction prices above the asset's maximal payout.
Speculative asset bubbles can arise, even if the asset's dividend distribution and terminal value are common knowledge.
Experience reduces, but may not eliminate, the formation of speculative bubbles.
With risk neutral investors, an asset's fundamental value is the present discounted value of expected dividends (plus discounted terminal value, if applicable).
At the beginning of the game, each student receives some amount of cash and a number of shares in a company. At the end of each round, each share pays a dividend (either high or low, each with 50% chance) whereas interest is paid on cash. During each round, students participate in a double auction to buy or sell the shares.
We set the default parameters so that a) the asset's expected and maximal payoffs are easily calculable; and b) the default parameters are conducive to bubble formation.
By default, dividends of $1.00 and $0.40 each occur with 50% chance, there is no interest on cash, and the asset has no terminal value. This means that the asset's maximal payout is $1 times the number of dividends remaining, $15 in the first of 10 periods. Expected payout (and thus, the fundamental value, assuming risk neutrality) is $0.70 times the number of remaining dividends, $10.50 in the first of 10 periods. Transaction prices above the asset's maximal payout are consistent with a speculative asset bubble.
Experienced players are less likely to form a speculative asset bubble. On the other hand, increasing starting cash balances seems to facilitate bubble formation.
Inducing a flat fundamental value is a great way to combine this game with a lesson on asset pricing. With a positive interest rate, you get a constant fundamental value across periods by setting the terminal value equal to the present value of the infinite stream of expected dividends (i.e. the expected dividend by the interest rate on cash). With the default dividends ($1.00 and $0.40 each with 50% probability), setting a 10% interest rate and a $7 terminal value results in a $7 fundamental value in all periods.
In this context, you can increase the likelihood of a bubble by simultaneously increasing both the interest rate and the dividends. For example, doubling both the expected dividend and the interest rate does not affect the asset's fundamental value, but does appear to increase the likelihood of speculative bubbles.
An asset purchase at a price above the discounted value of the higher dividend in all rounds (plus the discounted terminal value) is consistent with speculative demand. A string of such purchases is evidence of a speculative asset bubble.
The main graph (Figure 1) makes it easy to identify a speculative bubble. Each transaction's price is depicted in the graph, as are two additional benchmarks. The blue line shows the asset's expected value if held to the final round. Absent speculative demand, this would be the price with risk neutral investors. The red line is asset's payout if the higher dividend is realized each period. While transactions between the two lines can be explained by risk-loving preferences, prices above the asset's maximal payout can only be justified by a belief of later resale at a price above the asset's maximal payout (i.e., speculative demand).
Note that when a speculative bubble crashes, transaction prices often dip below the asset's expected fundamental value.