Fungicide resistance and misinformation: A game theoretic approach

Fungicide resistance is a serious problem for agriculture today. This analysis provides additional insight into the strategic behavior of farmers when their fungicide use generates negative intertemporal production externality in form resistance. We find that encounter this type externality, they choose levels exacerbate examine compensation mechanism which farmer reduces exchange transfer. use; however, misinformation about severity distortions. one-sided could lead to socially optimal levels, makes less necessary. In addition, we show both are misinformed, below level depending on pessimistic beliefs La résistance aux fongicides est aujourd'hui un grave problème pour l'agriculture. Cette analyse fournit aperçu supplémentaire du comportement stratégique des agriculteurs lorsque leur utilisation de génère une externalité intertemporelle négative sous forme fongicides. Nous constatons que les font face à ce d'externalité, ils choisissent niveaux qui exacerbent la examinons mécanisme dans lequel agriculteur réduit l'utilisation en échange d'un transfert. Ce fongicides; cependant, désinformation sur gravité distorsions. unilatérale pourrait amener choisir socialement optimaux, rend le d'indemnisation moins nécessaire. En outre, nous montrons deux sont mal informés, inférieurs au niveau fonction leurs croyances pessimistes sévérité The sector uses control disease and preserve crop yield quality. However, many most effective fungicides has become prevalent, compromising (for more details, see Lucas et al., 2015). For instance, powdery mildew pervasive well-documented. Grape United States (US) particularly dependent upon fungicide-based control, with 95 % yields attributable (Gianessi & Reigner, 2006). Powdery prominent pest species crops including grape wheat, development presents significant in, example, Canada, China, Europe, US (see Vielba-Fernández 2020 specific examples). resistance1 requires increased applications same not only cost implications farmers, but also environmental health consequences.2 Pimentel (2005) estimates costs pesticide than $1.5 billion year alone. challenge addressing part collective action problem, since farmer's can neighboring experience (see, e.g., Sexton 2007); therefore, efforts mitigate it benefit from understanding choices selection levels. our paper, aim answer following questions: (i) How do adjust usage facing resistance? (ii) Does there exist help reduce (iii) does affect performance mechanism? Similar Regev al. (1983), Cornes (2001), Ambec Desquilbet (2012), Martin (2015), Herrmann (2016), address tension between needing while future periods as result its use. Along (1983) mainly concerned developing tool facilitate internalization resistance, externalities generally. A central contribution examination It belongs second two policy approaches discussed by (1983); namely, rather examining subsidy3 study allows voluntarily restrict receive corresponding loss profits.4, 5 Farmers who provide compensation.6 several advantages. promotes cooperation among via monetary transfer profit participating. be used general context where farmers' affects effectiveness periods, is, present. Our approach similar those proposed by, Bhat Huffaker (2007), Liu Sims (2018). (2007) develop self-enforcing cooperative agreement variable payments an mammal population. (2016) side payment incentivize producers coordinate transboundary invasions spatial-dynamic model. (2018) determine timing risk-reduction strategies problems ecological change, using bioinvasion discuss possibility induce coordination. Lemarié Marcoul (2018), users coordination, define coordination considering impact profits, under certain conditions manufacturers have incentives share information likelihood begin two-stage complete-information game representative before ultimately extending scenario accounting misinformation. first stage, simultaneously profit-maximizing input all other inputs. again must externality. necessary stage achieve output one (thus illustrating cumulative nature resistance). consider discrete-time choice renders distinct others such Cobourn (2019), dynamic settings. Like limit model two-stages because sufficient effects arise subsequent period (while providing analytic solutions infer behavior). heed warning Finger (2017) avoid designing single isolation. Therefore, Skevas (2013), insights effect inputs well. technology emphasize dependence fungicide, unlike (2015). context, mitigation constrained cannot aggravate quantitative resistance; access alternative apply present consequences next period. paper applicable associations especially continue pesticides contribute Currently, generally equipped accurate Resistance Assessment, Mitigation Extension (FRAME) Network, motivation efforts, emphasizes that, “There currently no system monitor or predict usually identified after management failure.”7 To current scenario, extend allow misinformation, incorrectly assess (one-sided two-sided misinformation). four separate cases: without extension includes designed lower aggregate variation severity, (iv) By setting misinformed evaluate distortions generated Under complete information, drives own (or below) requiring neighbor even further. Given reduction transfer, anticipated detrimental performance; contexts resistance: completely informed misinformation) (two-sided if becomes difficult either fungicide. findings suggest ameliorating crucial and, thus, Further, restricting resistance,8 then require greater informed. implies make costly enact mechanism. accessible educational programs advance knowledge full participation mechanism.9 remainder proceeds follows. Section 2 describes model, social planner's 3 contains 4 concludes. generates, form: i restricts provided j compensates lost profits. discussion 2.2. Next, what occurs As benchmark, compensation. Profits 1 given Equations (4) (5), respectively. assume α > β $\alpha >\beta$ , sensitive combined, + < +\beta <1$ function satisfies decreasing returns scale. simplicity, = =\frac{1}{2}$ $\beta =\frac{1}{4}$ facilitates provision meaningful results.16 solve backward induction. each k chooses maximize respective profits 2. obtains best-response capturing shown proof Proposition Appendix A1 (all proofs relegated appendix), increasing represents adjustment second-period stemming 1. value equilibrium results presented proposition. 1.In absence mechanism, unambiguously higher relationship stems manifests differences (in 1) planner (e.g., association) maximizes discounted farmers. focus welfare sum π t ∗ $\pi _{kt}^{*}$ at time t. Considering damage pollution through overuse) extra societal cost. lemma, associated compare them (Proposition 1). Lemma 1.The following. benchmark case, difference explained Each internalizes ignores other's external helps internalize. That considers maximization, internalize responds reducing periods. Regarding inputs, observe x S O $x_{i1}^{SO}$ $x_{i1}^{*}$ . decrease period, y $y_{i1}^{SO}$ decreases overall so need compared case internalized. coincide ( $x_{i2}^{SO}=x_{i2}^{*}$ ), expected ends section, propose induces enter according best j. constrains application R $y_{i1}^{R}$ 2.17 rooted Coasian approach, affected parties reach setting, agrees any due induction, 2.The Implementing lowers admissible parameter values strictly positive transfers, T C I $T^{CI}$ occur discount factor, δ, sufficiently low δ $\delta <\frac{1}{2}$ ). weight assign (note symmetric farmers). indicates compensate requested When more, first-period θ, values. severe (i.e., θ increases) order Depending appendix details). Table 1, across various scenarios p w $p=w=1$ 0.2 0.2$ c z 0.5 $c=z=0.5$ ; include compensation, relatively mild high 0.25 $\theta =0.25$ 0.75 0.75$ respectively). varies ) =0.75$ cases considered increases increases. Across contained within incentivizes i's would Particularly, optimal. Finally, $y_{i1}+y_{j1}$ third row optimal, fourth 0.37 0.42), 0.23 0.30, seventh eighth Farmer faces compensating i, estimates, holds incorrect about, severity; reported growers Oliver (2021). Kuklinski (2000), “confidently hold[s] wrong beliefs.” confidence distinguishes uncertain farmer, therefore distinctly. knows true misinformed. situation if, j, experienced expert consultants. knowing wrongly believes m _m$ (where ≠ _m\ne \theta$ If _m >\theta$ describe pessimistic, <\theta$ optimistic. Otherwise, maintain assumptions structure summarize 3. 3.In previous too high, relative know (because forced externality). how j's corollary explicitly compares these Corollary 1.Without insufficient _m>2\theta$ coincides _m=2\theta$ Intuitively, twice reality farmer), Figure Region A). Conversely, excessive amount _m<2\theta$ optimistic farmer; B). socially-optimal actually leads select outcome, making unnecessary.18 visually graph horizontal axis vertical axis. comparisons independent ¯ $y_{i1}^{*}=\bar{y}_{i1}$ informed, _{m}>\theta$ proposition, applying 4.When misinformation), Farmers' comparison, 2, different 0.5. 0.09 0.15 0.24 0.34 0.17 $0.09+0.15 0.17+0.17$ fact, amount, hold 0.199 $T 0.199$ 0.188 0.188$ use, diminishes severity. beliefs, _m=0.25$ overuses (compared use) underuse (Table 1), transfers 0.189 0.199) 0.194 0.188). subsection, being particular, (farmer j) _{m}^{i}$ _{m}^{j}$ respectively), _{m}^{i},\theta _{m}^{j}\ne $ \theta _{m}^{i}= asymmetric _{m}^{i}\ne proposition 5.In 3, j's) ^{i}_m 2\theta$ ^{j}_m respectively).19 behave will overuse distortionary magnified neither information. Recall gets 6.When γ − $\gamma 1+\delta _{m}^{i}+(1-\delta ω $\omega +2\delta (1-\delta _{m}^{j} +2 \delta ^2 (higher increases, _{m}^{i}>\theta further _{m}^{i}=0.5$ {SO}^{CI}$ assuming 0.3 ${\theta =0.3}$ simplicity continuity =0.2$ indicate exacerbates observed except slightly _{m}^{j}=0.25$ applies 35 44 0.40, sixth (when reduced surpasses possess size turn depicts blue curve _{m}=\theta balanced yellow illustrates _{m}^{j}=0.75$ (recall =0.3$ (positive quadrant). absolute value) belief ^{i}_{m}=0.5$ ordinal relation possesses optimistic, analysis, two-period game. willingly receives doing so. scenarios, compel Without fail success critically depends available excessively (insufficiently) whether (pessimistic, respectively) 3), These signal importance improving participate Efforts communicate essential mitigating Relatedly, it. connected demanding restriction neighbor. reverse true. cases, believe higher. pessimistic; already accept terms exchange, assignment aleatory symmetric, association decide role natural extension. relevant An avenue work field experiment reductions achieved place. decisions shed light gratefully acknowledge financial support USDA-NIFA-SCRI program award number 2018-03375 titled “FRAME: Mitigation, Network Wine, Table, Raisin Grapes.” very thankful advice, suggestions, comments editor, Corinne Langinier, anonymous referees, Félix Muñoz-García, Michelle Moyer, Shanthi Manian. grateful AAEA Virtual Meeting, AERE-SEA AERE-EEA 2021 Montreal Workshop Resource Environmental Economics. Note $y_{i1}$ ∂ * 32 $\frac{\partial y_{i1}^{\ast }}{\partial }=-\frac{ p^{4}w^{4}\delta }{32c^{2}z^{2}(1+\delta )^{3}}$ values) $y_{i2}$ y_{i2}^{\ast }=\frac{p^{4}w^{4}(1-\delta )}{32c^{2}z^{2}(1+\delta <\frac{1}{\delta }$ satisfied ≤ \le 1$ definition). 16 y_{i1}^{SO} }{\partial }= -\frac{\delta p^4 w^4}{16 c^2 z^2 (1+2 )^3}$ $y_{i2}^{SO}$ <\frac{1}{2 y_{i2}^{SO} \frac{p^4 w^4 (1-2 )}{32 positive). perfectly $x_{j2}$ $y_{j2}$ _{j2}$ Results equivalent found A.1, =\theta combinations β. satisfied, (relatively elasticity fungicide) consider. 1: Sensitivity Analysis Case \frac{1}{2}$ \frac{1}{5}$ ≥ $y_{i1}^{*}\ge y_{i1}^{SO}$ 2: \frac{2}{3}$ 3: \frac{1}{4}$ ∼ $\widetilde{y}_{i2}^{\ast }>\widetilde{y}_{i1}^{\ast \widetilde{x}_{i2}^{\ast }>\widetilde{x}_{i1}^{\ast ∈ 0 ,\gamma \in (0,1)$ \widetilde{y}_{i1}^{\ast }}{ \partial }=-\frac{p^{4}w^{4}\delta 64 \widetilde{y}_{i2}^{\ast }=\frac{p^{4}w^{4}(1+\gamma )(1-\delta )}{64c^{2}z^{2}(1+\delta definition. $y_{i2}^{\ast }>y_{i1}^{\ast $x_{i2}^{\ast }>x_{i1}^{\ast } }=-\frac{p^{4}w^{4}(1+\delta (2-\theta ))}{ 32c^{2}z^{2}(1+\delta }=\frac{ p^{4}w^{4}(1-(2+\delta )\theta +2}$