BASIC MODEL. In the previous chapters, I have developed a concept that aims at explaining the evolution of dynamic capabilities in technology-based new ventures by linking the strategic management framework to entrepreneurial learning and organisational development and change. In the course of this effort, I have derived various hypotheses that support this concept and the underlying approaches and theories. To denote the links between the concept and the different hypotheses, I provide a summary of the different findings from the theoretical part of this study in this third chapter.
BASIC MODEL. The Xxxxxxxxx model is based on a single period setting. Suppose we invest X0 amount of money in an asset at time t = 0 and after a period of time, we sell the asset at price X1. Here, we denote the ratio R = X1 X0 as the return on the asset. Then, the rate of return on the asset is defined as µ = X1 − X0 X0 = R − 1. Thus, we have X1 = RX0 = (1 + µ)X0. Now consider the case with n securities. Let X0 be the initial amount of money we are holding at time t = 0. We wish to distribute this amount of money into n asset and the amount that we assign to asset i is X0i = uiX0 where ui denotes the i=1 fraction of investment in asset i, so Σn ui = 1. Let the total return on asset i be Xx and then the payoff from this portfolio after a period of time is n n X1 = Σ RiuiX0 = X0 Σ Riui i=1 i=1 so the total return R is Σ
BASIC MODEL. We follow Xxxxx and Xxx (2013), who extend the concept of Perfectly Coalition-Proof-Xxxx Equilibrium (PCPNE) advanced by Xxxxxxxx et al. (1987) to settings in which overlapping coalitions may coexist. We show this extension in Appendix A. It employs the perfectly coalition-proof concept to the sets of players produced by the union of intersecting (i.e., overlapping) sets of players. Suppose that N = {1, 2,3} denotes the set of all players. In addition to N , the subsets of the set of all players are the singletons, {1},{2},{3} and the pairs {1, 2} , {1,3} , {2,3} . The standard coalition-proof concept is applicable to all coalitional structures except to the overlapping ones, in which one nation is a hub. The extended concept of Xxxxx and Xxx (2013) is applicable to the overlapping coalitional structures: it is employed over the union of the overlapping bilateral coalitions; namely the set {1, 2,3} . Consider, for example, the coalitional structure in which nation 1 is a hub and nations 2 and 3 are spokes; that is, the coalitions{1, 2} and{1,3} coexist in equilibrium. The Xxxx equilibrium for this structure is coalition-proof if and only if there is no individual nor collective incentive to deviate; that is, player 1 has no incentive to exit either coalition, and players 2 and 3 have no incentives to exit their respective coalitions in order to stand alone or to form the bilateral coalition {2,3} . The latter is one of the possible self-enforcing sub-coalitions that can be produced from the set {1, 2,3} . The game considered here is a strategic network formation game. We formulate a multistage game, in which the first stage is a participation stage. If the joint R&D agreements prohibit transfers, the game contains two stages: following the participation stage, there is a contribution stage. If the joint R&D agreements allow transfers, the game also includes a third stage in which coalitions implement transfers. Formally, the participation stage can be described as follows. For a game where N = {1, 2,3} , a pointing game Γ is a list (N ,(Si ) ,Ui ) , where S = {0,1}N \{i} = {0,1}×{0,1} for i∈N each i ∈ N (a representative element si = {sij , sik }∈ Si describes the countries that country i is pointing towards to initiate an agreement, and sij = 1 means that country i selects country j while sij = 0 means that country i does not select country j ) and Ui (si , s−i ) = ui ({i, j} ⊂ N : sij = s ji = 1) for each i ∈ N . We later extend the model to allow for a ...
