CEO-Bench: Can Agents Play the Long Game? — part 6/7

Cleaned-text code points [77902, 93008). Bibliography omitted here; source.md includes it.
Competitor events are disabled before t comp start t_{\mathrm{comp}}^{\mathrm{start}} and after t comp end t_{\mathrm{comp}}^{\mathrm{end}} . Let τ \tau be the last event day. The mean interval is Δ ¯ t = { m Δ  Δ , t < t Δ switch , Δ , t ≥ t Δ switch , \bar{\Delta}_{t}=\begin{cases}m_{\Delta}\Delta,&t<t_{\Delta}^{\mathrm{switch}},\\ \Delta,&t\geq t_{\Delta}^{\mathrm{switch}},\end{cases} (32) with a separately configured minimum interval Δ min \Delta_{\min} . If t − τ < Δ min t-\tau<\Delta_{\min} , no event occurs; otherwise E t ∼ Bernoulli ⁡ ( 1 / Δ ¯ t ) . E_{t}\sim\mathrm{Bernoulli}(1/\bar{\Delta}_{t}). (33) When an event occurs, a base boost is sampled and scaled over the run: B t sample = clip ⁡ ( LogNormal ⁡ ( μ B , σ B ) , B min , B max )  ( α B + ρ B  t − t B start T B ramp ) . B_{t}^{\mathrm{sample}}=\operatorname{clip}\!\left(\mathrm{LogNormal}(\mu_{B},\sigma_{B}),B_{\min},B_{\max}\right)\left(\alpha_{B}+\rho_{B}\frac{t-t_{B}^{\mathrm{start}}}{T_{B}^{\mathrm{ramp}}}\right). (34) t comp start t_{\mathrm{comp}}^{\mathrm{start}} and t comp end t_{\mathrm{comp}}^{\mathrm{end}} bound the active competitor window, τ \tau is the last event day, Δ ¯ t \bar{\Delta}_{t} is the current mean interval between competitor events, E t E_{t} is the event indicator, m Δ m_{\Delta} slows early events, Δ \Delta is the baseline interval, t Δ switch t_{\Delta}^{\mathrm{switch}} is the interval switch day, and Δ min \Delta_{\min} prevents events from arriving too close together. μ B , σ B \mu_{B},\sigma_{B} parameterize event size, B min , B max B_{\min},B_{\max} bound it, t B start t_{B}^{\mathrm{start}} is the boost-ramp start day, and α B , ρ B , T B ramp \alpha_{B},\rho_{B},T_{B}^{\mathrm{ramp}} control magnitude scaling over the run. Together these terms simulate rival launches that are not perfectly periodic, but become more serious as the market matures. The simulator also models adaptive competitor catch-up to the agent’s unreleased global development and R&D gains. Let H t global H_{t}^{\mathrm{global}} be the unreleased shared-quality bank. With u t global ∼ Uniform ⁡ ( u min global , u max global ) u_{t}^{\mathrm{global}}\sim\mathrm{Uniform}(u_{\min}^{\mathrm{global}},u_{\max}^{\mathrm{global}}) , B t = max ( B t sample , u t global H t global ) , H t + global = H t global − 𝟙 { u t global H t global > B t sample } u t global H t global . B_{t}=\max\!\left(B_{t}^{\mathrm{sample}},u_{t}^{\mathrm{global}}H_{t}^{\mathrm{global}}\right),\qquad H_{t+}^{\mathrm{global}}=H_{t}^{\mathrm{global}}-\mathbb{1}\{u_{t}^{\mathrm{global}}H_{t}^{\mathrm{global}}>B_{t}^{\mathrm{sample}}\}\,u_{t}^{\mathrm{global}}H_{t}^{\mathrm{global}}. (35) Thus B t B_{t} is the applied competitor quality boost, B t sample B_{t}^{\mathrm{sample}} is the exogenous shock, u t global u_{t}^{\mathrm{global}} is the random catch-up fraction, and H t + global H_{t+}^{\mathrm{global}} is the remaining shared-quality bank after the event. The event boost is at least the stationary sampled shock but can be larger when the agent has accumulated large unreleased global improvements. If the adaptive term wins, the competitor consumes that fraction of the bank. This simulates competitors copying or matching broadly visible product improvements: large general advances can invite stronger competitive responses than small incremental changes. Targeted development has a parallel group-specific adaptive component: D g , t target = v g , t  H g , t target , v g , t ∼ Uniform ⁡ ( v min , v max ) , H g , t + target = H g , t target − D g , t target , D_{g,t}^{\mathrm{target}}=v_{g,t}H_{g,t}^{\mathrm{target}},\qquad v_{g,t}\sim\mathrm{Uniform}(v_{\min},v_{\max}),\qquad H_{g,t+}^{\mathrm{target}}=H_{g,t}^{\mathrm{target}}-D_{g,t}^{\mathrm{target}}, (36) where H g , t target H_{g,t}^{\mathrm{target}} is the unreleased targeted-development bank, v g , t v_{g,t} is the group catch-up fraction sampled between v min v_{\min} and v max v_{\max} , D g , t target D_{g,t}^{\mathrm{target}} is the targeted drift shock, and H g , t + target H_{g,t+}^{\mathrm{target}} is the remaining targeted bank after catch-up. The applied event shifts all customers’ curves upward by adding B t B_{t} to global quality expectation, κ g  B t \kappa_{g}B_{t} to group g g ’s expectation, and D g , t target D_{g,t}^{\mathrm{target}} to group g g ’s expectation. Here κ g \kappa_{g} is group competitor reactivity. The intuition is that competitors are partly exogenous and partly responsive: broad R&D attracts broad catch-up, while targeted work is harder for competitors to fully copy but can still leak into group expectations. This simulates real competitive pressure where segment-specific improvements can create more durable advantage than broad, easily observed product gains.

#### Macroeconomic schedule.

The hidden macro state is an Ornstein–Uhlenbeck process around a sinusoidal PMI cycle ( Uhlenbeck and Ornstein, 1930 ; Szimayer and Maller, 2004 ; Koenig, 2002 ) : μ t = \displaystyle\mu_{t}={} μ PMI + A PMI  sin ⁡ ( 2  π  t / P PMI + ϕ ) , \displaystyle\mu_{\mathrm{PMI}}+A_{\mathrm{PMI}}\sin\!\left(2\pi t/P_{\mathrm{PMI}}+\phi\right), (37) PMI t + 1 = \displaystyle\mathrm{PMI}_{t+1}={} clip ⁡ ( PMI t + η PMI  ( μ t − PMI t ) + σ PMI  ϵ t , PMI min , PMI max ) . \displaystyle\operatorname{clip}\!\left(\mathrm{PMI}_{t}+\eta_{\mathrm{PMI}}(\mu_{t}-\mathrm{PMI}_{t})+\sigma_{\mathrm{PMI}}\epsilon_{t},\mathrm{PMI}_{\min},\mathrm{PMI}_{\max}\right). with ϵ t ∼ 𝒩 ⁡ ( μ ϵ , σ ϵ 2 ) \epsilon_{t}\sim\mathcal{N}(\mu_{\epsilon},\sigma_{\epsilon}^{2}) . μ t \mu_{t} is the current cycle target, μ PMI \mu_{\mathrm{PMI}} is the baseline PMI, A PMI A_{\mathrm{PMI}} is cycle amplitude, P PMI P_{\mathrm{PMI}} is cycle period, ϕ \phi is phase, η PMI \eta_{\mathrm{PMI}} is mean-reversion speed, σ PMI \sigma_{\mathrm{PMI}} is shock scale, and PMI min , PMI max \mathrm{PMI}_{\min},\mathrm{PMI}_{\max} bound the index. Intuitively, demand oscillates through a PMI-like expansion-and-contraction cycle, while the OU update makes temporary surprises fade back toward the current cycle phase. This simulates macroeconomic background conditions that drift gradually but also contain noise. For each customer group and macro-sensitive dimension d d , M g , d , t = max ⁡ ( M min , M 0 + β g , d  PMI t − PMI 0 PMI 0 ) . M_{g,d,t}=\max\!\left(M_{\min},M_{0}+\beta_{g,d}\frac{\mathrm{PMI}_{t}-\mathrm{PMI}_{0}}{\mathrm{PMI}_{0}}\right). (38) M g , d , t M_{g,d,t} is the macro multiplier, M 0 M_{0} is neutral, M min M_{\min} is its floor, β g , d \beta_{g,d} is group sensitivity, and PMI 0 \mathrm{PMI}_{0} is the neutral PMI reference. The dimension d d can represent macro-sensitive quantities such as lead flow, willingness to pay, or enterprise deal velocity, and different groups react with different sensitivities. The simulator uses real-time hidden PMI internally, while the agent sees only period averages published every D publish D_{\mathrm{publish}} days with delay D delay D_{\mathrm{delay}} . This simulates management under delayed economic indicators: the world has already moved before the agent receives clean macro data.

### A.7 Enterprise Sales and Negotiation

#### Offer evaluation.

Enterprise customers evaluate up to K offer K_{\mathrm{offer}} offered ( plan , price ) (\mathrm{plan},\mathrm{price}) options and choose the one with highest S i offer = Q i , p , t perc − Q i req  ( C ) , S_{i}^{\mathrm{offer}}=Q_{i,p,t}^{\mathrm{perc}}-Q_{i}^{\mathrm{req}}(C), (39) where K offer K_{\mathrm{offer}} is the maximum number of options the agent can present, Q i , p , t perc Q_{i,p,t}^{\mathrm{perc}} is the perceived quality of the offered plan, Q i req  ( C ) Q_{i}^{\mathrm{req}}(C) is the required quality at price C C , and S i offer S_{i}^{\mathrm{offer}} is offer surplus. Positive surplus means the proposed plan clears the customer’s price-quality bar. If the best offer is positive, the customer accepts. This simulates enterprise procurement evaluating a small menu of contract options rather than passively accepting a list price. Otherwise, the simulator computes C i max  ( Q ) = max ⁡ { C ≤ c i : Q i req  ( C ) ≤ Q } C_{i}^{\max}(Q)=\max\{C\leq c_{i}:Q_{i}^{\mathrm{req}}(C)\leq Q\} (40) where C i max  ( Q ) C_{i}^{\max}(Q) is the highest price the customer would accept at perceived quality Q Q , c i c_{i} is the customer’s budget ceiling, and the max operator searches for the price that is still justified by the offered quality. This is the reservation price implied by the same participation curve used for self-serve customers. This simulates a procurement ceiling: the customer may negotiate, but there is a maximum contract value that the perceived product quality can support. With sampled initial factor f i f_{i} and configured counter-offer decay γ α \gamma_{\alpha} , C i , r counter = C i max − γ α r  ( C i max − f i  C i max ) , C_{i,r}^{\mathrm{counter}}=C_{i}^{\max}-\gamma_{\alpha}^{r}\left(C_{i}^{\max}-f_{i}C_{i}^{\max}\right), (41) where C i , r counter C_{i,r}^{\mathrm{counter}} is the counter-offer on turn r r , f i f_{i} is the initial counter-offer fraction of the customer’s maximum acceptable price, and γ α \gamma_{\alpha} controls how quickly later counter-offers approach that maximum. Early counter-offers start below true willingness to pay; later turns move toward the customer’s maximum acceptable price. If the configured maximum turn count is exceeded, the customer stops responding. This simulates negotiation anchoring: buyers may reveal willingness to pay gradually rather than immediately offering their ceiling. Reply delays are also stochastic: d i , r reply ∼ 𝒟 i reply  ( d ¯ i / M g , deal , t , σ i d ) , d_{i,r}^{\mathrm{reply}}\sim\mathcal{D}_{i}^{\mathrm{reply}}\!\left(\bar{d}_{i}/M_{g,\mathrm{deal},t},\sigma_{i}^{d}\right), (42) where d i , r reply d_{i,r}^{\mathrm{reply}} is the delay before the customer responds, d ¯ i \bar{d}_{i} and σ i d \sigma_{i}^{d} are customer response-time parameters, 𝒟 i reply \mathcal{D}_{i}^{\mathrm{reply}} is the customer-specific reply-delay distribution, and M g , deal , t M_{g,\mathrm{deal},t} is the macro deal-velocity multiplier. Stronger macro conditions shorten expected delay by increasing the denominator, while slow conditions stretch sales cycles. This makes enterprise sales slower and less certain than self-serve conversion while still following the same underlying price-quality logic. The mechanism simulates procurement latency, stakeholder review, and macro-sensitive sales velocity.

### A.8 Costs and Cash Flow

#### Daily costs.

Daily operating cost combines fixed infrastructure, variable compute, operations, development, advertising, targeted actions, lead acquisition, and research charges: K t cost = \displaystyle K_{t}^{\mathrm{cost}}={} K κ t capacity + ∑ p χ p usage  U p , t use + x t ops + x t dev + X t target  -  ops + ∑ g x g , t target  -  dev + ∑ c , g x c , g , t ads \displaystyle K_{\kappa_{t}}^{\mathrm{capacity}}+\sum_{p}\chi_{p}^{\mathrm{usage}}U_{p,t}^{\mathrm{use}}+x_{t}^{\mathrm{ops}}+x_{t}^{\mathrm{dev}}+X_{t}^{\mathrm{target\text{-}ops}}+\sum_{g}x_{g,t}^{\mathrm{target\text{-}dev}}+\sum_{c,g}x_{c,g,t}^{\mathrm{ads}} (43) + N t lead  c lead + K t market + K t group + K t project \displaystyle+N_{t}^{\mathrm{lead}}c^{\mathrm{lead}}+K_{t}^{\mathrm{market}}+K_{t}^{\mathrm{group}}+K_{t}^{\mathrm{project}} K κ t capacity K_{\kappa_{t}}^{\mathrm{capacity}} is the fixed cost of capacity tier κ t \kappa_{t} , χ p usage \chi_{p}^{\mathrm{usage}} is per-usage cost for plan p p , U p , t use U_{p,t}^{\mathrm{use}} is usage on that plan, x t ops x_{t}^{\mathrm{ops}} and x t dev x_{t}^{\mathrm{dev}} are global operations and development spend, X t target  -  ops X_{t}^{\mathrm{target\text{-}ops}} is targeted support spend, ∑ g x g , t target  -  dev \sum_{g}x_{g,t}^{\mathrm{target\text{-}dev}} is targeted development spend across groups, ∑ c , g x c , g , t ads \sum_{c,g}x_{c,g,t}^{\mathrm{ads}} is acquisition advertising spend across channels and groups, N t lead  c lead N_{t}^{\mathrm{lead}}c^{\mathrm{lead}} is the per-lead acquisition charge, and the three K K terms are market research, group research, and research-project charges paid that day. This cost equation simulates the operating budget of a software company, where fixed infrastructure, variable compute, staffing, marketing, and research all consume cash through different channels. The cash update is B t + 1 = B t + Y t sub + ∑ i Y i , t ads − K t cost , B_{t+1}=B_{t}+Y_{t}^{\mathrm{sub}}+\sum_{i}Y_{i,t}^{\mathrm{ads}}-K_{t}^{\mathrm{cost}}, (44) where B t B_{t} is company cash, Y t sub Y_{t}^{\mathrm{sub}} is subscription revenue, ∑ i Y i , t ads \sum_{i}Y_{i,t}^{\mathrm{ads}} is in-product ad revenue, and K t cost K_{t}^{\mathrm{cost}} is total operating cost. This is the main strategic coupling in the simulator: growth, quality, and reliability can create future revenue, but they consume cash immediately. The mechanism simulates startup runway management, where the agent must decide when to burn cash for future growth and when to preserve liquidity to avoid bankruptcy.

## Appendix B Rule-Based Baseline Strategy and Configuration Search

We use the rule-based baseline as a non-LLM point of comparison for the agent results in Section 3.2 . The baseline is intentionally simple: it commits to a fixed pricing book, fixed product-quality and advertising spend levels, and a fixed customer targeting rule. It does not use market research, enterprise negotiation, social media analysis, promotions, or language-model calls.

At the start of a run, the policy sets prices, model tiers, and usage quotas from one price book. During each simulated week, it selects target customer groups from its target rule. If cash is above a configured floor, it applies a small global development spend of $200/day, a fixed targeted development spend for each selected group, and, starting on day 20, a fixed targeted advertising spend for each selected group. Advertising is placed on the highest-yield channel for the selected group under the simulator’s fixed channel table. Operations spend is set to max ⁡ ( 100 , 0.05  n t ) \max(100,0.05n_{t}) dollars/day, where n t n_{t} is the current active subscriber count. The policy adjusts capacity by at most one tier per week toward the cheapest tier whose capacity covers recent average usage at 80% utilization. This simulates a simple operating playbook: spend proportionally to current scale, focus on a small target market, and avoid complex adaptation or hidden-state inference.

The configuration search is the Cartesian product of the options in Table 4 , giving 24 configurations. Each configuration is evaluated for the full 500-day simulation with seed 42. The best configuration uses the mid price book, targets S1 only, uses the heavy spend package, and has a $100K cash floor; the $300K cash floor gives the same result for this seed. The traced replay of this configuration ends with $15.76M in cash.

## Appendix C Comparison to Vending-Bench 2 Curves