Rodrigues António, Koeppl Heinz, Ohtsuki Hisashi, Satake Akiko
School of Computer and Communication Sciences, Ecole Polytechnique Fédérale de Lausanne (EFPL), Lausanne 1015, Switzerland.
J Theor Biol. 2009 May 7;258(1):127-34. doi: 10.1016/j.jtbi.2009.01.005. Epub 2009 Jan 17.
We studied a two-person game regarding deforestation in human-environment relationships. Each landowner manages a single land parcel where the state of land-use is forested, agricultural, or abandoned. The landowner has two strategies available: forest conservation and deforestation. The choice of deforestation provides a high return to the landowner, but it degrades the forest ecosystem services produced on a neighboring land parcel managed by a different landowner. Given spatial interactions between the two landowners, each landowner decides which strategy to choose by comparing the expected discounted utility of each strategy. Expected discounted utility is determined by taking into account the current and future utilities to be received, according to the state transition on the two land parcels. The state transition is described by a Markov chain that incorporates a landowner's choice about whether to deforest and the dynamics of agricultural abandonment and forest regeneration. By considering a stationary distribution of the Markov chain for land-use transitions, we derive explicit conditions for Nash equilibrium. We found that a slow regeneration of forests favors mutual cooperation (forest conservation). As the forest regenerates faster, mutual cooperation transforms to double Nash equilibria (mutual cooperation and mutual defection), and finally mutual defection (deforestation) leads to a unique Nash equilibrium. Two different types of social dilemma emerge in our deforestation game. The stag-hunt dilemma is most likely to occur under an unsustainable resource supply, where forest regenerates extremely slowly but agricultural abandonment happens quite rapidly. In contrast, the prisoner's dilemma is likely under a persistent or circulating supply of resources, where forest regenerates rapidly and agricultural abandonment occurs slowly or rapidly. These results show how humans and the environment mutually shape the dilemma structure in forest management, implying that solutions to dilemmas depend on environmental properties.
我们研究了一个关于人类与环境关系中森林砍伐的两人博弈。每个土地所有者管理一块单一的土地，土地利用状态为森林、农业或废弃。土地所有者有两种可用策略：森林保护和森林砍伐。选择森林砍伐会给土地所有者带来高回报，但会降低由另一个土地所有者管理的相邻土地上产生的森林生态系统服务。考虑到两个土地所有者之间的空间相互作用，每个土地所有者通过比较每种策略的预期贴现效用，来决定选择哪种策略。预期贴现效用是根据两块土地上的状态转变，考虑当前和未来将获得的效用而确定的。状态转变由一个马尔可夫链描述，该链纳入了土地所有者关于是否砍伐森林的选择以及农业废弃和森林再生的动态。通过考虑土地利用转变的马尔可夫链的平稳分布，我们推导出了纳什均衡的明确条件。我们发现，森林的缓慢再生有利于相互合作（森林保护）。随着森林再生加快，相互合作转变为双重纳什均衡（相互合作和相互砍伐），最终相互砍伐（森林砍伐）导致唯一的纳什均衡。在我们的森林砍伐博弈中出现了两种不同类型的社会困境。在不可持续的资源供应下，最有可能出现猎鹿困境，即森林再生极其缓慢但农业废弃相当迅速。相比之下，在持续或循环的资源供应下，囚徒困境可能出现，即森林再生迅速且农业废弃缓慢或迅速发生。这些结果表明了人类与环境如何相互塑造森林管理中的困境结构，这意味着困境的解决方案取决于环境特性。
