Abstract
In this paper, a dynamic rent-seeking game incorporating policymaker cost and competition intensity is considered. On the basis of the political environment and rent-seekers with incomplete information set, the locally asymptotic stability of Nash equilibrium is proved. The competition intensity and policymaker cost could enlarge the stability region of Nash equilibrium. The higher the competition intensity is, the more the opponent’s expenditure reduces the player’s success probability, which is beneficial to the maintenance of Nash equilibrium. The higher the policymaker cost is, the less easily both players succeed and the more stable the rent-seeking market is. As the competition parameter decreases or the expenditure parameter increases, there will be chaos in a rent-seeking market. Chaos control is in order to stabilize the equilibrium of the rent-seeking game.
Highlights
To make the research more realistic, scholars put forward kinds of rationality expectations, which have formed the cornerstone of this field, such as bounded rationality, adaptive expectation, naıve rationality, and local monopolistic approach (LMA). is kind of research could be applied to motive the competition and changes in the biological systems over time
Our study aims at analyzing a dynamic rent-seeking game with policymaker cost and competition intensity
When the parameters u1, u2 are in the stability region S, in the dynamic rent-seeking game, players adjust the expenditure for rent-seeking based on a gradient rule and achieve the Nash equilibrium of complete information static rent-seeking game with complete rationality . e Nash equilibrium could be used to analyze and forecast the result of the rent-seeking game
Summary
Godwin et al improved Tullock’s lottery model of rentseeking [7]. ey checked a policymaker cost N for supplying a rent value V (>N) and a rent-seeking competition intensity α ∈ Ey checked a policymaker cost N for supplying a rent value V (>N) and a rent-seeking competition intensity α ∈ E intersection point of the two response function curves is Nash equilibrium (Re1, Re2) of the game. E Nash equilibrium of complete information static rent-seeking game with policymaker cost and competition intensity exists. From the two lemmas above, we could prove that the static game of complete information has only one symmetric. We assume that (R1, R2) is the Nash equilibrium; if R1 ≠ R2 from Lemma 2, we know, Ri ∈ [0, (V − N)/α], i 1, 2. (9) Checking formula (4), (αR1 + N)V R2 + αR1 + N, we have the following equation:. Erefore, a dynamic rent-seeking game problem with limited rationality needs to be considered The rent seekers’ complete information and rationality are not always satisfied. erefore, a dynamic rent-seeking game problem with limited rationality needs to be considered
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