When Cicadas Sing: Modeling Stock Market Herd Behavior with Game Theory

The herd effect in stock markets traces back to Keynes’s "beauty‑contest" analogy, where a critical mass of participants triggers collective behavior.

The phenomenon is essentially conformity; before the herd effect fully emerges, a preparatory stage can be illustrated by the cicada‑chirping analogy, where a few insects start calling and gradually induce mass chorusing.

In the stock market, a few investors initially buy a stock, prompting others to follow; over time, the stock attracts increasingly many investors, both rational and bounded‑rational, leading to a full herd effect analogous to a synchronized cicada chorus.

Chinese research on original investment‑decision theory is scarce, especially regarding the unique psychology of domestic investors. This paper focuses on psychological factors influencing Chinese investors’ decisions and seeks to extract a general investment method usable even by those unfamiliar with fundamental or technical analysis.

Mathematical Analysis of One Cicada’s Call Triggering Another’s

Assumption 1: Every investor has both the desire and the ability to purchase stocks.

Assumption 2: The accumulated demand state variable is a monotonically increasing convex function.

Assumption 3: One investor’s purchase increases other investors’ demand; if the demand exceeds a threshold, those investors also start buying.

Modeling two participants, let the variable represent the proportion of desired investment relative to maximum capacity. The investment desire of each participant is a monotonic convex function of the other’s accumulated desire, leading to a threshold‑driven activation similar to cicada chirping.

Extending to N investors, each participant’s desire evolves similarly: when one’s desire reaches the threshold, it triggers others, mirroring the cicada‑chorus mechanism.

Game‑Theoretic Analysis of Cicada Synchronization

Consider two investors in a stock. If one buys and the other does not, the non‑buyer gains nothing. Assuming each investor’s action influences the other, we define mixed‑strategy probabilities for holding the stock. The payoff matrix shows that simultaneous holding or simultaneous selling yields the highest expected returns, leading both investors to choose the same action.

When many participants are involved, the dynamic equilibrium can be expressed with differential equations describing the rate of change of the proportion of investors holding versus selling. Equilibrium occurs when these rates become zero, indicating stable proportions.

Equilibrium of Synchronized Cicada Calls and Investment Decisions

In an imperfect‑information market, only sellers know the cost C and only buyers know the value V. Sellers set a price function of C, buyers set a bid function of V. The resulting Bayesian equilibrium determines optimal strategies.

The analysis concludes that the optimal investment timing is to enter before the cicada chorus (herd effect) fully develops and exit before the Bayesian equilibrium is reached, while rigorously controlling position size and risk.

Because large institutions often detect the initial “chirp” earlier than retail investors, they trigger the subsequent mass chorus. Retail traders should therefore manage leverage, adopt short‑term positions during market declines, and execute quick entry and exit to avoid deep drawdowns.

Source: Lin Aihua & Zhang Shaohua, “Cicada‑Chirping Phenomenon and Stock Market Investment Decisions”.