vault backup: 2025-11-21 15:31:28
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---
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id:
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aliases: []
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tags:
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- authorship/original
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- destiny/permanent
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- status/draft
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- type/daily
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title: 2025-11-21
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---
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# 2025-11-21
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## 2025-11-21 10:11
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> [!quote] [ELECTRI's Industry Benchmarking Tool - ELECTRI International](https://www.electri.org/research-overview/electris-industry-benchmarking-tool/)
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> ### Hours Burned vs. Hours Earned
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>
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> Definition:
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> Comparison between portion of project estimated hours complete
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> compared with the actual hours spent on the task.
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> This is the labor performance factor
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> (needs to reference the labor factor used at bid time for a full comparison).
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This is a terribly problematic metric.
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If a project went over its material budget
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despite standard rigorous oversight
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where would you first look,
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construction or estimating?
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In almost all cases the safer bet is estimating.
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Why should labor be different?
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Wherever there is budget variance
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there is a persistent tendency to blame construction
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before estimating.
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[[purpose-of-construction-estimating#The Myth of Estimate Accuracy]]
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---
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id:
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aliases: []
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tags:
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- authorship/llm
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- destiny/fleeting
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- status/complete
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- topic/estimating
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- topic/risk
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title: Modeling Bid Prices Under Intrinsic Cost Uncertainty
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---
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# Modeling Bid Prices Under Intrinsic Cost Uncertainty
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> [!warning]
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> This text is almost entirely LLM output.
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> I don't intend to keep or use any significant portions of it.
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Consider a construction project characterized by an intrinsic but unknown final cost $C$.
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Prior to project completion, $C$ cannot be observed directly;
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instead the estimator possesses only a probability distribution over feasible outcomes.
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Let $(\Omega, \mathcal{F}, \mathbb{P})$ be a [probability space](https://en.wikipedia.org/wiki/Probability_space)
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describing the estimator's uncertainty,
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and define the true cost model as a non-negative random variable
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$$
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C : \Omega \to [0,\infty)
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$$
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with [distribution](https://en.wikipedia.org/wiki/Probability_distribution) $\mu_C$.
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The distribution $\mu_C$ summarizes all available information at the time of bidding,
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including quantities, labor productivity uncertainty,
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market conditions, subcontractor pricing variability,
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and correlation structures inherent to the estimator's assumptions.
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Although the natural mathematical representation of cost is thus a distribution,
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procurement mechanisms typically require that each bidder submit a single deterministic price.
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Denote this bid by
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$$
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B \in [0,\infty).
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$$
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> Read as
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> "$B$ is an [element](https://en.wikipedia.org/wiki/Element_(mathematics))
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> of the interval from zero to infinity, including zero."
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A bid $B$ may be viewed as the output
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of a pricing [functional](https://en.wikipedia.org/wiki/Functional_(mathematics))
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$$
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\Phi : \mathcal{P}([0,\infty)) \to [0,\infty),
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$$
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mapping a cost distribution $\mu_C$ to a scalar.
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Examples of such functionals include:
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### 1. Risk-neutral expectation
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$$
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\Phi(\mu_C) = \mathbb{E}[C],
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$$
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> Read as "Phi of mu sub C equals the expected value of C."
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where $\mathbb{E}[\cdot]$ denotes the [expected value](https://en.wikipedia.org/wiki/Expected_value).
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### 2. Risk-adjusted expectation
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$$
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\Phi(\mu_C) = \mathbb{E}[C] + \lambda\sqrt{\mathrm{Var}[C]},
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$$
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> Read as "Phi of mu sub C equals the expected value of C plus lambda times the square root of the variance of C."
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where $\mathrm{Var}[C]$ is the [variance](https://en.wikipedia.org/wiki/Variance)
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and $\lambda>0$ is a risk-loading parameter.
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> This mirrors mean--variance pricing common in portfolio theory.
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### 3. Quantile-based pricing
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$$
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\Phi(\mu_C) = Q_p(C),
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$$
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> Read as "Phi of mu sub C equals the p-quantile of C."
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where $Q_p$ is the $p$-[quantile](https://en.wikipedia.org/wiki/Quantile)
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of the distribution.
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### 4. Utility-maximizing bid
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Under a bidder [utility](https://en.wikipedia.org/wiki/Utility) function $U$,
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$$
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\Phi(\mu_C) = \arg\max_{b\ge0} \; \mathbb{E}[\,U(b - C)\,].
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$$
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> Read as "Phi of mu sub C equals the argument b greater than or equal to zero
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> that maximizes the expected value of U of b minus C."
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> [$\arg\max$](https://en.wikipedia.org/wiki/Arg_max) is the value of $b$ that maximizes the expression.
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***
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The central tension is:
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* The ontologically correct representation of project cost prior to execution is a **probability distribution**, whereas
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* The procurement mechanism requires a **deterministic scalar**.
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The study of such pricing functionals $\Phi$ sits within
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[stochastic optimization](https://en.wikipedia.org/wiki/Stochastic_optimization),
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[risk measures](https://en.wikipedia.org/wiki/Risk_measure),
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and [mechanism design](https://en.wikipedia.org/wiki/Mechanism_design).
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Understanding how different choices of $\Phi$
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compress and distort the underlying uncertainty $\mu_C$
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has direct implications for bidder profitability, competitive strategy,
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and how risk is allocated across the construction market.
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+29
-1
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## Scope
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This note is intended to describe bid process strategy
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especially in terms of [[strategy#Auction Theory]],
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especially in terms of [[auction-theory]],
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which specifically addresses the competitive bid format
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typical of construction project award.
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@@ -38,3 +38,31 @@ Bidders will accept a lower payout or even a loss
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in order to retain employees.
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**Backlog Deficit** drives up **Utility of award**
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## Factors Brainstorm
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This is a list of semi-independent factors
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relevant to the contractors decision of if and how to bid.
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### Key
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* `> [!info]` --- **Fact:** an indisputable truth or term definition
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* `> [!important]` --- **Logical Consequence**
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* `> [!tip]` --- **Relationship**
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* `> [!success]` --- **Desirable Outcome**
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* `> [!failure]` --- **Undesirable Outcome**
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> [!info]
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> The exact cost of a construction project is **uncertain**
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> until it is completed.
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> [!info]
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> Customers request bids as a
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> [!tip]
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> Spending _more_ time on estimates
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> [!tip]
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> Estimating _more_ projects leads to _more_ opportunities for award.
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> Estimating _fewer_ projects leads to _fewer_ opportunities for award.
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+22
-6
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they have no incentive to reveal errors
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as they can simply plead ignorance if the error is discovered.
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## Incentives
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I strongly oppose any project-based incentive structure for estimators.
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Such a structure is at odds with the [[purpose-of-construction-estimating]],
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and is an example of a [perverse incentive](https://en.wikipedia.org/wiki/Perverse_incentive).
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This behavior should be regulated by an accompanying _disincentive_ structure,
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but equivalent punishment becomes unfeasible
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before monetary rewards become effective.
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The absolute worst disincentive an estimator faces is termination,
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which, with fully-remote options available, is only an inconvenience.
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The timeline to recognize an estimate was deliberately misrepresented
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is not much shorter than that of the project.
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Such incentives therefore create a [[game-theory|competitive game]]
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between the estimator and the employer
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where the employer is hopelessly outmatched,
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and the estimator's [[strategy#Strictly Dominant Strategy|strictly dominant strategy]]---
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resisted only by their moral conviction---
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is to abuse the system: to bid fast, lie often, take the bag, and leave.
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## Collaboration
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Estimation is a profession ripe for productive collaboration.
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@@ -80,9 +102,3 @@ to embrace the statistical aspects of our field.
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* Be competent with every tool available to you.
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* Always assume there is a better way to complete a given task.
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## Incentives
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I strongly oppose any project-based incentive structure for estimators.
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Such a structure is at odds with the [[purpose-of-construction-estimating]],
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and is an example of a [perverse incentive](https://en.wikipedia.org/wiki/Perverse_incentive).
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# Game Theory
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## Domains
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### Auction Theory
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[[auction-theory|Auction theory]] is a subset of game theory
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<!-- TODO: -->
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#### Reverse Auction
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In a reverse auction,
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bidders compete for the right to _sell_ a product or service.
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#### Sealed-Bid Auction
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Opposite of a conventional "open" auction,
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in a sealed-bid auction,
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bid prices are hidden from the bidders.
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[[uncertainty#Information]]
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<!-- TODO: -->
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## Terminology
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### "Solved" Games
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<!-- TODO: -->
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### Symmetry
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## Typical Games
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### Chicken
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| Player A \ Player B | Player B: Back Down | Player B: Hold Firm |
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|:------------------- |:-----------------------:|:-----------------------:|
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| Player A: Back Down | Tie \ Tie | Lose face \ Gain status |
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| Player A: Hold Firm | Gain status \ Lose face | Die \ Die |
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### Prisoner's Dilemma
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| Prisoner A \ Prisoner B | Prisoner B: Cooperate | Prisoner B: Defect |
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|:----------------------- |:---------------------------:|:-----------------------------:|
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| Prisoner A: Cooperate | Serve 1 year \ Serve 1 year | Serve 3 years \ Go free |
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| Prisoner A: Defect | Go free \ Serve 3 years | Serve 2 years \ Serve 2 years |
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### Stag Hunt
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| Hunter A \ Hunter B | Hunter B: Hunt Stag | Hunter B: Hunt Hare |
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|:------------------- |:--------------------:|:--------------------:|
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| Hunter A: Hunt Stag | Eat stag \ Eat stag | Go hungry \ Eat hare |
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| Hunter A: Hunt Hare | Eat hare \ Go hungry | Eat hare \ Eat hare |
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### Ultimatum Game
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### Dictator Game
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@@ -18,8 +18,6 @@ which would take far longer than allotted for bid,
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## The Myth of Estimate Accuracy
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<!-- TODO: -->
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This is a dangerous superstition
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which encourages unproductive conflict.
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@@ -27,6 +25,20 @@ Operations is blamed for failing to meet targets
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not intended for the purpose,
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...
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***
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Construction contract bids are inherently risky.
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Executives want to bid because construction can be profitable.
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Executives hire estimators to mitigate risk of loss.
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An estimator's value is determined by their
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An estimator's job is to mitigate
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Estimators downplay the
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## For Each Party
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### For the Solicitor
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+12
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The field of strategy is concerned
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with the optimal solutions of problematic scenarios.
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## Decision Theory
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## Domains
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Decision theory concerns
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### Decision Theory
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* ~~internal problems~~
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* ~~no competition~~
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* ~~internal optimization~~
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[[decision-theory|Decision theory]] concerns choices
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made by a single party, based on environmental conditions
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## Game Theory
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"Player vs. Environment"
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Game theory concerns decisions
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### Game Theory
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[[game-theory|Game theory]] concerns choices
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made in competition with other intelligent actors.
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Predictions of competitor behavior in bids and market movements
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are made with a game-theoretic lens.
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"Player vs. Player"
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## Terminology
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### Dominant Strategy
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A dominant strategy is one
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that results in the better outcome.
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### "Solved" Games
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### Strictly Dominant Strategy
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<!-- TODO: -->
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### Auction Theory
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Auction theory is a subset of game theory
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<!-- TODO: -->
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#### Reverse Auction
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In a reverse auction,
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bidders compete for the right to _sell_ a product or service.
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#### Sealed-Bid Auction
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Opposite of a conventional "open" auction,
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in a sealed-bid auction,
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bid prices are hidden from the bidders.
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[[uncertainty#Information]]
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<!-- TODO: -->
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@@ -29,6 +29,10 @@ by Douglas W. Hubbard
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* Certain Monetary Equivalent (CME)
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* also called Certainty Equivalent
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One or more curves referenced in the text are
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[Indifference curves](https://en.wikipedia.org/wiki/Indifference_curve)
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but not referred to as such.
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## Key Takeaways
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### Definition of Risk
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@@ -12,3 +12,20 @@ title: Uncommon Syntax
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* **i.e.** --- _id est_ ("that is")
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* **e.g.** --- _exempli gratia_ ("for example")
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## Symbols
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* $\therefore$
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* $\vdash$ --- turnstile,
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denotes logical consequence
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* $\vDash$ or $\models$ --- double turnstile,
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denotes [semantic](https://en.wikipedia.org/wiki/Semantic "Semantic") consequence
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> [!quote] [Double turnstile - Wikipedia](https://en.wikipedia.org/wiki/Double_turnstile)
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> read as
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> "[entails](https://en.wikipedia.org/wiki/Logical_consequence "Logical consequence")",
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> "[models](https://en.wikipedia.org/wiki/Model_theory "Model theory")",
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> "is a **semantic consequence** of"
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> or "is stronger than".
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