Model Setup Clause Samples

Model Setup. Similar to ▇▇▇▇▇▇▇▇▇▇▇▇▇ and Rysman (2009), I consider the following consumer level in- finite horizon dynamic optimization problem with a discount factor b. At each time period t (month in this case), each consumer i chooses either one of the currently available products, Jt , or chooses to defer purchase to a future period and continue to use the currently owned car or avail of other mode of transportation. Similarly, at period t + 1, the consumer chooses one of the Jt+1 products or opts for the outside option j = 0 so that she maximizes the sum of the expected discounted value of utilities conditional on her information at period t. Each product j ∈ Jt is characterized by observed characteristics x jt (e.g. manufacturer, size, reliability, etc.), the unobserved (by the econometrician) characteristic ξ jt , and the price p jt . Extending ▇▇▇▇▇▇▇▇▇▇▇▇▇ and ▇▇▇▇▇▇ (2009), I assume that products deterministically de- preciate at a rate of ▇ .▇ I assume that consumers are heterogeneous in their taste for product characteristics, price sensitivity and willingness to travel. To model this, I define consumer- specific random coefficients αi = (αx, αp, αd ) for car characteristics, price, and distance to the dealer, respectively. Following the literature, I assume that consumers are completely informed about all time t related information when making decisions at time t. Moreover, consumers have idiosyncratic shocks to their preferences for each product and in each period εi jt , which I assume as being i.i.d. across (i, j, t).7 Following the random coefficients discrete choice framework of ▇▇▇▇▇ et al. (1995), con- sumer i obtains the following one-period utilities for each available choice at time period t: 6λ is currently assumed to be the same across all cars. However, this can be relaxed to allow brand-varying depreciation rates.‌ 7Logit errors (and most i.i.d error terms) typically imply unrealistic welfare gains from new products (see ▇▇▇▇▇▇ 2002). ▇▇▇▇▇▇▇▇▇ and ▇▇▇▇▇▇ (2005) argue that this feature of the logit-based demand model make them inappropriate in contexts where consumers face a vastly different numbers of products over time. ▇▇▇▇▇▇▇▇▇ and Rysman recommend addressing this problem by including the log of the number of products, ln(Jt ), as a regressor. A coefficient of 0 on the associated parameter implies the logit model is well specified, whereas a coefficient of -1 implies “full crowding," so there is no demand expansion effect from increasing ...

Model Setup. ‌ Three players, a dictator (D), an elite with a high initial endowment of power (H), and an elite with a lower initial endowment of power (L), together form a regime. Each player’s type, τi > 0, is his power endowment. I use the following notation to measure the power disparity among the players: H’s initial endowment of power is fixed at H (τH ≡ H > 0); the dictator’s endowment is d > 0 larger than this (τD ≡ H + d) and L’s endowment is w ∈ (0, H) less (τL ≡ H − w). The dictator has the most power initially (which is why he is the dictator) and the high elite has more initial power than the low elite. Thus d (and d + w) can be interpreted as the dictator’s initial power advantage over the other two elites while w denotes the relative difference between elites H and L.

Model Setup. ∈ ∈ ∈ { }

Model Setup. We consider an inventory supply chain system in which a supplier manages the supply of a single product for the retailer. The demand at each period (dt) is stochastic, independent, and identically distributed (i.i.

Model Setup. ‌ Three players, a dictator (D), an elite with a high initial endowment of power (H), and an elite with a lower initial endowment of power (L), together form a regime. Each player’s type,τi, is his power endowment. H’s initial endowment of power is fixed at H (τH ≡ H); the dictator’s endowment is d > 0 greater than H’s (τD ≡ H + d) and L’s endowment is w ∈ (0, H) less than H’s (τL ≡ H − w). The dictator has the most power initially (which is why he is the dictator) and the high elite has more initial power than the low elite. Thus d can be interpreted as the dictator’s initial power advantage over the other two elites while 6 This is not to say that incomplete information regarding individuals’ strength and conflict actions is impossible. Indeed, in some cases a lack of information may lead to conflict. My model shows that incomplete information is not the only explanation for conflict and may be more applicable in regimes where there are institutions with the purpose of avoiding such information-induced conflicts (Boix and Svolik 2013) and yet conflicts are still observed (see ▇▇▇ and ▇▇▇▇▇▇▇ 2019 for a summary of elite-dictator conflicts despite institutions). Play takes place over the course of two rounds. First, the dictator chooses which elite to target for elimination or does not initiate conflict, ending the round. If a target is chosen, the dictator can make a take-it-or-leave-it offer, x ∈ [0, x¯], his post-conflict budget constraint, to the non-targeted elite to share the spoils of the conflict (conditional on winning) with that elite in exchange for the elite’s support in a coalition against the target.7 The dictator’s bud- get, x¯, is the total amount of power he would have if he won the conflict: the combined power of the dictator and his target. The non-targeted elite can choose to accept the dictator’s offer and join a coalition with the dictator, join the targeted elite, or remain out of the conflict. The dictator (or coalition) and target(s) then participate in a contest where the probability that each side wins is the difference between their relative power plus mean-zero noise; e.g. participant (or coalition) i wins the conflict if τi ≥ τj + ϵt where ϵt ∼ U [−a, a] independent of the round. Thus the probability that participant or coalition i wins is 5є(τi − τj). While the likelihood of winning is based on the power differential between the opponents, I assume all conflicts are uncertain.8 If a coalition formed, whichever side won the co...

Model Setup. We propose a dynamic game Γ with J +1 players that illustrates the essential elements of interactions between a brand name firm B (player 1) which is protected by a patent and J ≥ 1 potential generic challengers (G1, . . . , GJ ). Our game is designed to capture the market authorization rules and main features of P2D cases described earlier and stylized below. (1) There are two periods, period 1 which is pre-patent expiration, and period 2, which is post- patent expiration period. Alternatively, period 2 starts if the patent is declared invalid by a court. In period 2, we assume a competitive N-opoly ensues among the J + 1 firms, and there are no authorized generics in this period, as there is no need for a licensing agreement. (2) In the second period, all J generics produce the drug but the profits and/or market shares are not equal as the order of entry matters, i.e., one of them has a first mover advantage. Without loss of generality we assume that the second through the last generic all earn the same profit (which is less than that of the first generic entrant). (3) In period one, the J potential entrants can sequentially contest entry by filing for marketing authorization. The branded firm can offer a payment to a challenger to stay out of the market during period one (a P2D deal), and grantees the order of entry in the post-patent period as long as the patent is not invalidated by another challenger (order of entry is not guaranteed if the patent is invalidated).7 (4) If at any stage a challenger (say the jth) does not accept a P2D deal and wins the court case (patent is invalidated), that challenger enters immediately in period one. However, the remaining J − j entrants can only enter in period two.8 7For instance, the branded firm can always allow a generic to use its own production facilities to achieve all regulatory market approval requirements and enter just before other generic firms enter (▇▇▇▇▇▇, 2010). 8This assumption of an effective duopoly in period one allows us to model exclusivity period clause in the US or any de (5) Finally, if the jth firm wins the court case, the brand can opt to launch an AG via any (or even all) of the previously paid-off firms. If the branded launches an AG, period one consists of a triopoly. Based on the stylized rules above, the game is as follows. The patent can be challenged in any of the Γj stages of Γ game by the generic challenger ▇. Each stage Γj has the same structure, which is depicted in the Figures...

Model Setup. For the purpose of this study we use the latest version of TBEST (4.4), which was developed and upgraded by the State of Florida Department of Transportation (FDOT) in 2016. The software is available for download at ▇▇▇.▇▇▇▇▇.▇▇▇. We use the latest update on the socioeconomic data package that includes the 2014 American Community Survey 5-Year Estimates, the 2014 InfoUSA Employment data, and the 2015 Florida Department of Revenue Parcel-level Land Use. The software also employs the TBEST 2016 Land use model with default control parameter values (including bus capacity = 40 seats, a market capture buffer distance of 0.25 mile, etc.) and default service level attributes (i.e. no changes implied in headways, number of arrivals, park-n-ride parking capacities, etc.). Furthermore, in order to comply with STOPS results, the model is run for year 2015 (i.e. no growth rates are set). TBEST provides a user friendly graphical interface which interoperates with ESRI ArcGIS software. The unit of analysis in TBEST is a transit system, which comprises its extent (i.e., what counties are included), parcel data, and imported routes from the GTFS files. Within the software environment, the user can easily manipulate any of the socio-demographics, route-level attributes, stop-level characteristics, or transit service patterns in order to evaluate different scenarios (Figure 6).

Model Setup. For this study, the Southeast Florida (SEFL) Regional STOPS model developed in 2016 by AECOM and Connetics Transportation Group (CTG) was adopted. The model covers Palm Beach, Broward, and Miami-Dade Counties. As part of this effort, the team developed a user interface to automate the preparation of certain STOPS input files for any fixed-guideway transit project in the tri-county region. The model was calibrated to base year 2015, which had a total of 504,119 unlinked trips in the study area. The package provides all the required input files readily available, including the CTPP and census files, regional SED forecast files and highway skims, and GTFS files. Figure 5 provides a list of input files.